V Conference of the Italian Society of Statistical Physics - SIFS

Complex component systems are collections of discrete units such as species, words, genes, whose observed realizations are naturally summarized by component counts. Many empirical laws have been observed in those systems, such as Taylor's law, Zipf's law, and Heaps' law. Domain-specific mechanisms are often employed to explain their emergence but, despite their ubiquity, a unifying framework remains elusive. Here we propose such framework showing that, when observables are in the form of component counts, many scaling laws emerge as generic consequences of statistical convergence in large, heterogeneous systems. Taylor's law, for instance, reflects a crossover between sampling noise and genuine system heterogeneity, while Zipf's and Heaps' laws arise from the convergence of order statistics and distinct component counts under heavy-tailed but otherwise generic priors. Moreover, the resulting scaling laws, which we predict theoretically and verify across dozens of complex component systems from biology to linguistics, are largely distribution-agnostic and often transient. Our work thus suggests that these ubiquitous patterns are better interpreted as baseline statistical limit theorems instead of fundamental principles that require tailored generative explanations.

In the context of complex networks, designing a null model that preserves certain properties of the original network is a fundamental problem. While for binary bipartite networks, the problem has been solved by the Curveball algorithm, which preserves the degree of each node exactly, for weighted bipartite networks, finding a null model that strictly preserves some features of the original network is still an open challenge. We developed a microcanonical algorithm that preserves exactly the degree and the strength of each node in a weighted bipartite network. The algorithm is based on an edge-swap procedure that combines three different moves: weight shuffling, simple edge swap, and bridge edge swap. The algorithm has been built to guarantee that the underlying transition matrix of the Monte Carlo Markov chain is symmetric, which is a crucial property to obtain an unbiased sample of random graphs. We also empirically validated our algorithm, showing that it produces an unbiased sampling of graphs. Finally, we also provide a heuristic method to estimate the mixing time of the MCMC.

Complex systems tend to exhibit out-of-equilibrium dynamics over a broad range of timescales. A key theory challenge is to understand the features of this out-of-equilibrium behavior from the properties of the attractors of the system’s dynamical equations. Mean-field theories of spin glass dynamics offer elegant examples, linking phenomena such as aging to the properties of special families of stationary points of the underlying free-energy landscape, that attract the dynamics at large times. However, these insights apply mainly to systems to which one can associate such landscapes. It is an open question how to extend these ideas to high-dimensional non-conservative systems (such as biological neural networks, large ecosystems) whose dynamics is not landscape optimization. In this talk, I will present a simple model of a high-dimensional system with non-reciprocal interactions whose out-of-equilibrium, chaotic dynamics can be characterized analytically at long times. I will discuss its dynamical phase diagram and I will compare it to the statistical distribution of the many, unstable fixed points of the dynamical equations. The talk is based on joint work with Samantha Fournier, Alessandro Pacco and Pierfrancesco Urbani.

We show that systematic particle rotations in a fluid composed of disk-shaped spinners can spontaneously lead to phase separation. The phenomenon arises out of a homogeneous and hydrostatic stationary state, due to a pressure feedback mechanism that increases local density fluctuations. We show how this mechanism induces phase separation, coined as Rotation Induced Phase Separation (RIPS), when the active rotation is not properly counterbalanced by translational friction. A low density phase can coexist with a dense chiral liquid due to the imbalance between pressure and stress transmitted through chiral flows when a significant momentum transfer between rotational and translational motion can be sustained. As a consequence, RIPS is expected to appear as a general nonequilibrium phenomenon in chiral fluids.

Cities keep growing and host more than half of the global population. Despite their importance, there are no robust empirical laws describing city spatial dynamics. In [1], employing recent remote sensing data, we studied the growth of 19 cities over 30 years using population as control variable. When focusing on the largest component, we find that variations of population and built area are essentially proportional. However, when looking in a given direction, there are strong deviations to the square-root law expected in the isotropic case. By employing the framework of surface growth, we reveal that cities interface follow are anomalously intrinsically rough. Their local roughness is characterized by a scaling exponent equal to about 0.54. Other exponents are widely spread. We also observed seemingly universal, stretched-exponential fluctuations. These observations raise many physical questions; we discuss some of them concerning surface growth through strongly polydisperse deposition in [2]; a recent modified Eden based model reproducing the empirically observed results was proposed in [3]. [1] Marquis, U., Artime, O., Gallotti, R., & Barthelemy, M. (2025). Universal Roughness and the Dynamics of Urban Expansion. Phys. Rev. Lett., 135(18), 187403. [2] Marquis, U., Gallotti, R., & Barthelemy, M. (2026). Beyond dynamic scaling: rare events break universality. https://arxiv.org/abs/2604.01820 [3] Hendrick, M., Trique, M., & Manoli, G. (2026). Disorder Crossover in Urban-Front Growth. https://arxiv.org/abs/2604.21437

Understanding how complex networks respond to perturbations is essential to reveal their functional organization in all possible dynamical regimes. Existing information–thermodynamic approaches rely largely on diffusive descriptions, which implicitly constrain the diversity of responses that a system can exhibit. However, real-world networks often operate far from equilibrium and display rich, transient behaviors under perturbations. We show that diffusion-based frameworks impose a fundamental limitation: the entropy associated with network responses cannot increase in time, ruling out the emergence of enhanced functional diversity. To overcome this restriction, we develop a general information-thermodynamic theory of network response along arbitrary dynamical trajectories, based on a density-matrix formalism with a time-dependent evolution operator. We derive a normalization-preserving flow equation and demonstrate that it admits a variational foundation in terms of an information-theoretic least dissipation principle, establishing a direct correspondence with non-equilibrium thermodynamics. Applying the framework to synthetic and empirical networks coupled to nonlinear dynamics, we find regimes of positive entropy production that are inaccessible to diffusive approximations. Our results provide a unified theoretical basis to quantify how structure and dynamics jointly shape network responses, opening the way to trajectory-based extensions of information thermodynamics for complex systems.

We study rare events in time-correlated stochastic processes, focusing on the emergence of single big jump effects. The main part of this contribution concerns time-integrated observables in the Ornstein-Uhlenbeck (OU) process. Using an excursion-based mapping to a continuous-time random walk, we analyze the statistics of A=∫vn(t) dt where v(t) is the velocity following OU dynamics and n>0 positive integer number. We show that the large-deviation properties of A are governed by the statistics of the area accumulated during a single excursion above the origin. The associated rate function exhibits anomalous scaling and reveals a dynamical phase transition between a regime dominated by typical Gaussian fluctuations and a rare-event regime controlled by a single large excursion. In the latter case, the tail of the distribution is fully captured by a single big jump mechanism, providing a clear physical interpretation of the breakdown of standard large-deviation scaling in correlated dynamics. We conclude by briefly outlining recent extensions of the single big jump framework beyond the OU process, where perturbative corrections to the big jump principle allow one to describe moderate deviations in systems with stretched-exponential statistics, bridging typical fluctuations and extreme events.

In the study of stochastic processes, identifying the parity under time-reversal is essential to verify detailed balance, and to compute the entropy production rate (which is, otherwise, ambiguously defined). While in many cases the correct time-reversal symmetry is suggested by physical intuition, for generic processes the identification is not trivial: as a result, systems at thermal equilibrium may be mistakenly interpreted as non-equilibrium ones. We focus on the reversible deterministic dynamics of a slow variable coupled to many degrees of freedom acting as a thermal bath. We show that the time-reversal symmetry of the slow variable is preserved when passing to an effective stochastic description, independently of the nature of the bath. In turn, for generic 2-dimensional continuous Markov processes, we provide a criterion to identify the time-reversal parity rules under which the dynamics is at equilibrium (if any). The case of the Lotka-Volterra model is discussed as an example.

We study a finite one-dimensional lattice where nearest neighbour sites can exchange mass with an asymmetric local rule whose preferred di- rection is a random quenched variable à la Sinai. For any strength of the asymmetry, the total mass localizes around the minimum of a suitable poten- tial. For any realization of the disorder we obtain the stationary mass profile. For closed boundary conditions, the average over disorder profile is the arcsin law.

Neural networks are the fundamental tools of modern machine learning. They process information by loading it in the activations of the so-called input neurons: the information flows along the architecture of nested layers until the output is reached, where the decision takes place. This latter information processing can be interpreted as a discrete mapping that is ultimately shaped by the underlying network's topology. For this reason, studying neural networks from the fundamental standpoint is of interest to statistical physicists and for the complex systems' community at large. One obvious extension of the usual neural models amounts to consider hypergraphs as the backbone for the interactions. Working in this generalized setting, we will show that neural hypergraphs, if properly parameterized, have performances which are at least comparable to those reported for standard neural networks, but crucially without the need of deploying a neural activation function (usually indispensable for modern neural models). Furthermore, we will prove that, in some learning contexts, hypergraph models perform better than their network counterparts, achieving better accuracies despite having access to the same training samples.

Perturbations in disordered systems have dramatic effects both in the structure of low energy states that get completely reshuffled by small perturbations. This leads to chaotic dependence of the Gibbs state and aging reinitialization upon changes in control parameters. This fragility of the Gibbs states is strongly related to the emergence of critical Long Range Order of Spin Glass type. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Non-perturbative phenomena are present when 1 ~ ∆H ≪ N , being ∆H the coupling Hamiltonian and N the system size. In this talk I will consider the effect of very tiny perturbations in disordered systems and study (1) the formation of strong correlations in weakly coupled systems, (2) the fluctuations leading to size corrections in the Sherrington-Kirkpatrick model, (3) The stability of spin-glass RSB states in Dyson-lattice hierarchical spin glasses.

The scaling limit where both the size of the training set $P$ and the width $N$ of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks. However, extending these non-perturbative results from shallow architectures to deep non-linear networks has proven very challenging. Here we present a surprisingly effective \emph{approximate} approach to predict the generalization performance of Bayesian multi-layer perceptrons (MLPs) and of fixed depth $L$ on arbitrary high-dimensional data. We propose an equivalent Wishart Ansatz to capture the dominant stochastic fluctuations of the hierarchical empirical kernels of MLPs. This allows us to perform a large deviation analysis for the partition function of MLPs in the proportional limit, expressed in terms of a renormalized NNGP kernel. In this description, even strong representation learning in the proportional limit is encoded in at most $L$ scalar order parameters, determined self-consistently. Extending the approach to convolutional architectures (CNNs), we identify a hierarchical local kernel renormalization mechanism, which encodes more complex data-dependent transformations of the large-width kernel in CNNs due to finite-width effects. We test our effective theory against sampling experiments from the Bayesian posterior of finite deep neural networks with depths up to $L =10$ and $P~10^3$ on classic benchmark datasets, finding overall very good agreement together with two distinct types of systematic deviations.

Multitask learning, in which multiple auxiliary tasks are used to train a network to improve the generalization error of a specific task, has been used in many machine learning fields to improve network performance. We study this problem in the large-input limit of the multi-output teacher–student setting, in which the dynamics of online stochastic gradient descent are well described by a system of differential equations. We find the analytical solution for the corresponding linear model, expanding on the adaptive filters literature, and study the behavior of models trained with different activation functions, showing that dynamical effects dominate the solution.

The Slow Science Manifesto challenges the prevailing "publish or perish" culture in Academia and research, arguing that it undermines the quality, integrity, and societal value of scientific work. We advocate for a shift to more thorough research practices that allow scientists the time needed for deep thinking, careful literature review, and meaningful collaboration. The manifesto envisions a scientific ecosystem based on cooperation rather than competition, where the contribution and value of a scientist are not only measured through bibliometric indices.

During this session the Assembly of the Members of the Italian Society of Statistical Physics - SIFS will take place and only SIFS members can attend.

In this talk, I will review some of Amos Maritan’s many contributions to polymer physics with a special emphasis on the most recent results.

Inspired by the formation of bigels, we developed a bond percolation model that yields multiple percolating clusters in three dimensions not only at the critical point, but also above it. Our simulations suggest that, in the thermodynamic limit, there is no upper limit to the number of percolating clusters. We show that in finite systems the maximum number of percolating clusters that can be obtained grows logarithmically with the lattice size. For equal initial densities in the thermodynamic limit, all clusters percolate at the same threshold and exhibit critical exponents consistent with the critical exponents of standard percolation. The threshold depends linearly on the initial density of species and the maximum and minimum initial densities decay exponentially with the maximal number of spanning clusters. We also study a percolation model in which we occupy bonds randomly and each time a spanning cluster appears we remove it. The maximum number n_max of spanning clusters one can harvest in this way grows with the system size like a power-law with exponent d-d_f. Also, the variance of n_max and the size distribution of the remaining finite clusters grow like power-laws.

Neuronal cultures exhibit complex activity characterized by bursts and avalanches, displaying a bistable coexistence of scale invariance and synchronization that remains robust across different percentages of inhibitory neurons. In this work, we analyze experimental data from human-derived neuronal cultures with controlled excitation/inhibition ratios, providing a systematic characterization of avalanche statistics and their temporal organization. To describe this phenomenology, we propose a novel Kuramoto model for two interacting populations, introducing an inhibitory feedback term that captures the effective coupling between excitatory and inhibitory neurons while preserving the key features of single-population dynamics. The model reproduces the experimental findings, including the coexistence of scale-free avalanches and synchronization, their statistical properties and temporal correlations, and the emergence of an amplification-attenuation regime.

Metapopulation models are fundamental tools to understand how spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems. In this talk, we propose a mechanistic framework for deriving effective metapopulation and metacommunity models from individual-based ecological dynamics on arbitrary dispersal networks. We show that the resulting coarse-grained description features an effective dispersal kernel that encodes both microscopic dynamical parameters and network topology. Based on this framework, we are able to study how species persistence is affected by the homogeneity of the landscape, finding that heterogeneous habitats can support stable coexistence only above a certain level of spatial disorder. These results highlight how the interplay between network topology and spatial disorder shapes biodiversity in fragmented landscapes.

Ecological systems exhibit complex collective dynamics arising from dispersal, competition, growth, and resource constraints across multiple scales. Understanding how these processes shape ecosystem-level properties remains a central challenge, particularly when seeking empirically testable predictions. In this talk, I will discuss two recent examples of how statistical physics can be used to identify emergent observables that link ecological dynamics to measurable indicators of ecosystem state. First, a framework that unifies metacommunity theory and a generalized dynamical mean field theory to quantify species vulnerability in spatial communities. This framework captures the combined effects of dispersal heterogeneity and interspecific interactions and yields indicators that can be inferred from spatial abundance data. Second, a dynamical theory of forest communities that, using principles from metabolic scaling theory, connects growth, seed dispersal, and resource consumption processes to observed power-law scaling of tree-size distributions, providing interpretable indicators of ecosystem condition and revealing mechanisms through which local disturbances can propagate across large spatial scales. Together, these results illustrate how coarse-grained descriptions of ecological dynamics can generate tractable but testable predictions about resilience, vulnerability, and collective behavior in ecosystems.

We study the rheology of dense granular materials subjected to vertical vibration using numerical simulations of a stress-imposed vane rheometer. The effective viscosity increases with confining pressure, decreases with vibration amplitude, and exhibits a non-monotonic dependence on frequency: weakening is observed at intermediate frequencies but is lost at high frequencies. We show that the rheological response is governed by the balance between grain-scale agitation energy and the stabilizing effect of confinement. This framework reconciles previously observed trends in viscosity and friction weakening and emphasizes the central role of energy injection and dissipation in determining granular flow properties under vibration.

We develop a density-functional theory for solutions of associating polymers where attractions among charged monomers (stickers) are represented by local binary degrees of freedom, which are randomly placed along the chains. Extending the original Garel and Orland's field-theoretic scheme for single-chain systems to an ensemble of interacting chains, we give the exact formulations of the model in both cases of annealed and quenched distributions of charges which we solve at the mean field level. The solution roduces qualitatively different free energy functionals. In the annealed case, the theory naturally yields a nontrivial scalar order parameter for the fraction of bonded sticker monomers and a self-consistent mass-action law at the saddle point. By contrast, In the quenched case no independent bonding order parameter emerges and the main effect is a renormalization of the effective two-body interaction parameter. The formulation is microscopic at the Hamiltonian level and, within the same field-theoretic framework, provides a systematic starting point for fluctuation corrections beyond the mean field approximation.

Particle-based simulations of dense suspensions and jammed soft solids provide unique insight into self-organization during shear-thickening and upon flow cessation. I'll discuss how spatio-temporal analysis of microscopic structures, stresses and rearrangements reveals the origin of stress transmission, stress fluctuations, and residual stresses.

Self-organized criticality (SOC) will celebrate its fortieth anniversary next year. Although its potential relevance in neuroscience was acknowledged as early as in the 1990s, it was only after the discovery of neuronal avalanches in 2003 that SOC emerged—not without controversy—as a theoretical framework for interpreting collective brain dynamics. In this talk, I will offer an essential, forward-looking review of Lucilla de Arcangelis's contributions to the field of neuronal avalanches and brain criticality.

Microbiomes are intricate, dynamic communities of microorganisms that influence nearly every aspect of life. In this talk, I will outline key challenges in understanding their collective behavior and summarize recent results suggesting universal regularities in species-abundance patterns. I will discuss how interactions and non-trivial correlations shape community-level outcomes, and how microbial interaction networks often exhibit balanced structures that appear to be disrupted in dysbiotic states associated with disease. Many fundamental questions remain open, making microbial network complexity a rich and rapidly developing field for statistical physics and complex-systems research.

The increasing availability of large-scale textual corpora has opened new possibilities for data-driven, quantitative approaches to historical analysis using Natural Language Processing (NLP). However, diachronic corpora with historical relevance from the pre-digital era remain scarce and often incomplete. We present a quantitative approach to historical analysis based on the reconstruction and exploration of a diachronic corpus of around 600,000 articles from the Italian newspaper ”La Repubblica”, covering all the articles published from the 1st of January 1985 to the 31st of December 2000 - a period of major political, social, and geopolitical change in Italy and globally. Using NLP techniques, we analyze the text at both lexical and semantic levels across multiple temporal resolutions; we then apply tools from complex systems and statistical physics to trace shifts in media discourse over time. This unsupervised approach allows us to detect key transition periods, such as the transition from the First Republic to the Second Republic in Italy, or major international conflicts like the Gulf War or the Kosovo War, without relying on prior labeling. The results show how combining computational linguistics with ideas from complex systems can offer new quantitative insight into historical changes, opening up new paths for studying the dynamics of media and society through large-scale textual data.

The remarkable predictive power of the asymptotic state theory applied to nonequilibrium quantum dynamics relies on the ability to the cast the problem in the formalism of asymptotic states of quantum field theory, a framework which allowed the general analysis of systems with short-range interactions. At the same time, numerical studies of long-range interacting spin chains revealed dynamical features — including undamped oscillations at large time — quite analogous to those observed in short-range systems, suggesting that the domain of application of the asymptotic state theory could be further extended. Despite the additional analytical difficulties posed by long-range interactions, we show for the first time that such an extension can indeed be achieved in the case of quantum quenches. Considering d-dimensional homogeneous systems, we treat the long-range interaction as switched on by the quench and perform the derivation within the basis of asymptotic states of the short-range interacting pre-quench theory. This approach allows us to analytically determine the post-quench state and the one-point functions of local observables and to characterize their large-time behavior.

We discuss the $\nu=1$ Quantum Symmetric Simple Exclusion Process, a one-dimensional system of free fermions with time-dependent, spatially uniform stochastic hopping amplitudes. We investigate the out-of-equilibrium entanglement spreading following both global and inhomogeneous quantum quenches. For global quenches, we develop a diffusive quasiparticle picture that captures the full-time probability distribution of the entanglement entropy. For inhomogeneous quenches, we extend the framework of quantum generalized hydrodynamics to account for the underlying stochastic dynamics of the local quasiparticle occupation function.

Graph states play a central role in quantum information science, providing a unifying framework for measurement–based quantum computation, quantum error correction, and the study of many–body entanglement. When a graph structure is used to prescribe a set of pairwise interactions among qubits, the resulting state captures how the connectivity pattern influences the generation and distribution of quantum correlations. Understanding how entanglement responds to structural properties of the underlying graph is therefore of broad interest, especially when the graph is drawn from an ensemble. In this talk, I will rely on the entanglement distance, an entanglement quantifier whose geometric formulation has been summarized in [1] and recently applied to quantum systems defined on graph structures [2,3], to study graph–structured quantum states with non-local couplings induced by Katz-weighted interactions. In this setting, Katz weights encode the contribution of walks at all lengths, so that indirect connectivity, cycles, triangles and other recurrent patterns can contribute to the effective couplings. This provides a natural framework to investigate how entanglement is affected by network geometry beyond the nearest-neighbour structure encoded by the original graph. I will then apply this approach to random graph ensembles and study how the entanglement profile changes across different classes of random networks. [1] De Simone, L.; Capra, L.; Vesperini, A.; Rossi, L.; Di Cairano, L.; Franzosi, R. Geometric Aspects of Entanglement. Entropy 2026, 28, 299. https://doi.org/10.3390/e28030299 [2] De Simone L and Franzosi R 2025 Journal of Physics A: Mathematical and Theoretical 58 415302 URL: https://doi.org/10.1088/1751-8121/ae0bcb [3] De Simone L and Franzosi R Advanced Quantum Technologies n/a e00514 (Preprint https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/qute.202500514)

Quantifying the impact of hereditary transmission within lineage trees remains a fundamental challenge universal to a wide array of biological domains. In this talk, I will introduce and discuss the new concept of inheritance entropy, a quantity designed to gauge the hereditary structure of inactive cells across a lineage. We measured this entropy in 32 human stem cell clonal colonies, obtained from high-definition single-cell lineage tracing experiments, and showed that in the greatest majority of clones the entropy is decisively smaller than that of the corresponding non-hereditary ensemble, hence proving that variations in the proliferative power of stem cell lineages are determined by hereditary epigenetic factors that regulate cell-cycle exit. The method can also be employed to locate the specific node of the tree where a mutation in the probability of inactivity occurs, together with a determination of the lag between the mutation ultimately leading to inactivity and its actual expression. This framework can be used to assess in a robust, simple and model-agnostic way the hereditary origin of differential growth in any type of lineage trees.

Understanding how epigenetic patterns are established and maintained in living cells, and how these couple to 3D chromatin organisation, is a central open problem in biophysics. Here we introduce diluted chromatin-like magnetic polymer models in which only a fraction of monomers can carry epigenetic marks, while the remaining ones are neutral. This minimal polymer model captures the finite availability of epigenetic modifiers, and moves the system beyond an Ising description toward a different universality class. By combining mean-field theory and simulations, we show that dilution enables epigenetic phase separation, providing a robust physical pathway to first order transitions, which create epigenetic memory through metastability and phase coexistence. Epigenetic memory decays as a stretched exponential, revealing the coexistence of distinct timescales associated with mark spreading and chromatin dynamics. Our results highlight dilution as a key control parameter governing both the phase behavior and the memory capacity of epigenetic polymers.

We report the emergence of a novel macroscopic phase separation in a two-dimensional system of thermal inertial dumbbells driven into persistent rotation by a constant applied torque, interacting solely through repulsive forces. Through extensive molecular dynamics simulations, we map the phase diagram of the model and demonstrate that, above a threshold rotational activity, the system spontaneously demixes into a dilute liquid coexisting with a dense hexatic phase, with well-defined binodal and spinodal boundaries. By analyzing the Irving–Kirkwood pressure, we show that the underlying mechanism is fundamentally controlled by translational inertia: locally injected rotational kinetic energy is converted into translational motion at collisions and stored in the system in a density-dependent manner, producing a "hot dilute, cool dense" state. The resulting non-monotonic kinetic temperature gives rise to a Van der Waals loop in the pressure, rendering the homogeneous phase mechanically unstable. Quantitative agreement between the kinetic and Irving–Kirkwood pressures confirms that inertia is the dominant ingredient, and we show that the phase separation is progressively suppressed and disappears in the overdamped limit. Moreover, the coarsening kinetics follow the diffusive growth law R(t) ∼ t^(1/3) with dynamical scaling of the structure factor. Chirality additionally manifests through persistent edge currents along interfaces and, for isolated compact clusters, spontaneous rigid-body rotation about the center of mass with an angular velocity scaling linearly with the Péclet number — a behavior we rationalize through a simple balance of active and viscous torques.

Understanding how intelligent agents navigate competitive environments is a fundamental challenge in complex systems. We investigate the macroscopic dynamics of "strategic tension" across two structurally distinct model systems: chess and Go. We introduce a generalizable network framework to quantify this tension dynamically. In chess, tension emerges from the spatial network of interacting threats; in Go, from a network of group vulnerabilities and ownership instability under topological perturbations. In both domains, strategic tension is defined via the spectral properties of interaction matrices, rooted in topological entropy to quantify the exponential diversity of strategic trajectories. Analyzing games by human experts and state-of-the-art AI (e.g., Stockfish, AlphaGo), we reveal distinct profiles of complexity management. Engines consistently sustain significantly higher tension for longer durations than elite humans. This behavior reflects AI's capacity to defer immediate resolution and maintain high-dimensional latent options, scaling dynamically with computational depth. Conversely, human players actively simplify high-tension positions—an adaptive response to biological cognitive limits rather than a mere stylistic choice. Extending this framework from the hierarchical interactions of chess to preliminary data on the spatial dynamics of Go suggests that this divergence between artificial and biological problem-solving may be a universal phenomenon. Beyond cognitive insights, this framework enables the design of pedagogical AI tailored to human limits. Extrapolating to broader complex systems, such as economic markets or geopolitics, our findings suggest AI integration could fundamentally alter systemic stability, sustaining highly complex standoffs while drastically increasing the stakes of miscalculation.

In the first part of the talk, I will provide a pedagogical overview of recent literature focusing on quantum circuits and quantum cellular automata (QCA) as useful theoretical models in many-body physics, both in and out of equilibrium. I will highlight in particular the features that allow them to mimic the behaviour of realistic many-body systems, and explain their relevance for implementations in the quantum devices available today. In the second part of the talk, I will focus on some of my recent work on the subject, including exact results pertaining to the dynamics of entanglement in certain random circuits, and an experimental proposal to implement QCA in globally driven Rydberg-atom systems.

The quantum first-detection problem concerns the statistics of the time at which a system, subject to repeated measurements, is observed in a prescribed target state for the first time. Unlike in its classical counterpart, the measurement back action intrinsic to quantum mechanics can profoundly alter the system dynamics. Here, we show that the first-detection-time statistics for the Stark Hamiltonian is particularly sensitive to the the presence of many fermions. In particular, we show that while, in the single-particle scenario, a measurement protocol that detects the particle in its initial state strongly affects the time evolution at every measurement, in the many-particle case only measurements performed at integer multiples of the Bloch-oscillation period affect the system. We further show that measurements progressively spread the fermionic density and can therefore be used for state preparation.

In the last decades, the development of sophisticated cooling techniques has enabled the trapping of atomic gases in optical lattices, thus providing a suitable platform for the study of collective effects in many-body quantum systems. To a very good approximation, the behavior of bosonic atoms on a lattice can be described by an extended Bose–Hubbard (EBH) Hamiltonian, providing a paradigm of the superfluid-insulator transition, which has been extensively studied in the past by theory and simulations. Less attention has been paid to the behavior of the model in truncated lattices, with or without periodic boundary conditions. In this contribution we focus on the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids --- i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit. The dichotomy between superfluid-like and insulating-like behavior is then investigated also in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluid fraction and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in few-particle systems.

In recent years, Higher-Order Networks have emerged as a framework that extends the formalism of Complex Networks, enabling the description of interactions among multiple agents beyond simple pairwise relations. Examples of such higher-order structures are naturally encoded in simplicial complexes, which have been employed in a variety of contexts related to the modeling of complex systems. Here, we introduce a novel operator to describe a natural random walk process on a simplicial complex that models transitions across multidimensional structures. Walkers are allowed to wander across simplices of various dimensions, bridging nodes to edges, edges to triangles, and so on, within a nested organization that hierarchically extends to higher-order structures of arbitrarily large, yet finite, dimension. The asymptotic distribution of the walkers provides a natural ranking, enabling the assessment of the relative importance of simplices of different orders and types. We further apply this framework to compute the explorability of a simplicial complex, restricted to nodes, in the presence of a long-range stochastic teleportation term. The effect of noise appears highly beneficial for optimal search strategies when the walk occurs on higher-order structures, compared to what is observed on the corresponding binary graph. This illustrates an interesting example of the interplay between topological structures and the dynamical processes defined on them.

The study of spins and particles on graphs has applications across many areas, from time dynamics on networks to combinatorial optimization. In this talk, I will discuss the large n limit of the O(n) model on general graphs. The absence of translational invariance leads to an infinite set of saddle point constraints in the thermodynamic limit. I will show that the free energy at low and high temperatures T is controlled by two central graph-theoretic objects: the Laplacian matrix at low T and the Adjacency matrix at high T. Their interplay will be illustrated across several classes of graphs. On trees, on can obtain an exact solution in which the Lagrange multipliers depend only on the local coordination numbers. I will highlight the physical consequences using the example of a Y-junction. For graphs allowing a phase transition I will show that the singular part of the free energy is governed by the Laplacian spectrum, whereas the full free energy coincides with it only in the zero-temperature limit. I will conclude by presenting analogous results for the quantum version of the model.

Disclination lines in three-dimensional nematic liquid crystals generically form closed loops whose topology is classified by homotopy theory. While this classification successfully captures global topological features, it does not encode the geometry of the defect profile along the loop, which can strongly influence defect dynamics. Here, we propose a geometric description of nematic disclination loops using the Clifford algebra $\mathrm{Cl}(3,0)$. This approach naturally captures the geometry of the local defect profile, as well as changes along the loop, which is mathematically a $\mathrm{SU}(2)$ holonomy. Simulations of the dynamics of defect loops with specified geometries embedded in nematic liquid crystals demonstrate that loops nucleate the growth of "topological blobs" of defects, which later dissipate leaving uniform nematic textures. Self-twist of the defect profile leads to nucleation of additional linking disclination lines, with a simple arithmetic relation between total self-twist and linking number. In contrast, loops with an even number of discrete profile transitions generate patterns with threading between loops, but no linking. These results establish a direct connection between the geometric holonomy of a disclination loop and its subsequent evolution, and may be extendable to more complex order parameter manifolds, such as cholesterics or smectics.

Finite-width one hidden layer networks with multiple neurons in the readout layer display non-trivial output-output correlations that vanish in the lazy-training infinite-width limit. We leverage recent progress in the proportional limit of Bayesian deep learning (that is the limit where the size of the training set P and the width of the hidden layers N are taken to infinity keeping their ratio P/N finite) to rationalize this empirical evidence. In particular, we show that output-output correlations in finite fully-connected networks are taken into account by a kernel shape renormalization of the infinite-width NNGP kernel, which naturally arises in the proportional limit. We perform accurate numerical experiments both to assess the predictive power of the Bayesian framework in terms of generalization, and to quantify output-output correlations in finite-width networks. By quantitatively matching our predictions with the observed correlations, we provide additional evidence that kernel shape renormalization is instrumental to explain the phenomenology observed in finite Bayesian one hidden layer networks.

The dynamics of a Bose-Einstein condensate initialized in a far-from-equilibrium state can exhibit behavior that is reminiscent of fixed points in phase transitions—namely, self-similar scaling and universality. This phenomenon is referred to as a “non-thermal fixed point”. The properties of non-thermal fixed points enable predictions about the system’s relaxation dynamics, particularly the speed at which relaxation occurs. Dimensional analysis suggests that the relaxation speed exhibits universality—that is, counterintuitively, it does not depend on microscopic details such as the condensate’s density or interaction strength or on the exact initial state. Recent experimental results support this prediction (arXiv:2410.08204 [cond-mat.quant-gas]). In this poster, I will first introduce the concept of non-thermal fixed points and their connection to relaxation dynamics. I will discuss results based on numerical simulations and analytical approaches, addressing the question: “To what extent is the relaxation speed in a far-from-equilibrium Bose-Einstein condensate universal?”

A realistic model of a real world biological neural network would need to be both sparse and comprised of separate inhibitory and excitatory neuron populations. While dynamical mean field theory (DMFT) approaches exist separately for networks in the very sparse regime (degree $c \ll N$) and for diluted I-E networks, in our work we combine the two, using a population dynamics algorithm to sample the mean field path probability of very sparse I-E networks. We find that this approach correctly predicts the neuron currents, whereas the gaussian approximation fails. Moreover, this approach makes no assumptions about the degree distribution, and we show that even in the high connectivity limit $c \to \infty$, the network is affected by the degree fluctuations of an inhomogeneous distribution, diverging from the usual dense gaussian theory.

We introduce a technique that enables Neural-ODEs to approximate arbitrary velocity fields with a priori planted fixed-points. Specifically, a recipe is given to explicitly accommodate for a finite collection of points in the reference multi-dimensional space of the Neural-ODE where the velocity field is exactly equal to zero. In this way, the gradient-based training is rigorously constrained inside the prescribed hypothesis class while leaving the expressive power of the Neural-ODE unaltered. We rigorously prove the universality of the Neural-ODE under any local constraints in the velocity field and give a computationally convenient way of imposing the fixed points, testing it on two paradigmatic physical models.

The study of neuronal activity through electrophysiological recordings provides a framework to investigate brain function and how biological alterations may influence disease onset. Different analytical approaches across multiple brain scales (single neurons, neural networks, neural mass, and whole-brain activity) yield distinct biomarkers, offering insight into where and how system-level disruptions emerge in specific pathologies. Neuronal avalanches, consistently observed across these scales, suggest that brain dynamics operate near a critical point, leading to the emergence of scale-free distributions in both the size of recorded activity and the duration of bursts of coordinated activations. The occurrence of simultaneous activations across multiple neuronal components (e.g., brain regions in whole-brain analyses) correlates with the underlying connectivity among these components, providing a natural interpretation in terms of network interactions grounded in biologically measurable architectures. However, how neuronal activity, organized into avalanches, is structured in time—particularly in relation to the sequence of brain states (microstates) that the system traverses—and how the topological properties of brain architecture shape this temporal organization remain open questions. In this study, we analyzed magnetoencephalography (MEG) recordings from 30 healthy male and female subjects with no certified neurological disorders, during eyes-closed resting-state activity, within the framework of neuronal avalanche analysis. We find that the size of burst activations (defined as the integrated signal above threshold across all active brain regions during a bursting event) and the inter-avalanche silent time are not independent variables. The joint probability distribution of avalanche size conditioned on a given preceding silent time was estimated and compared with a reshuffled surrogate dataset, revealing significant temporal correlations. In particular, small avalanches are more likely to follow long silent periods, whereas large avalanches preferentially follow short silent intervals. These results provide the opportunity to distinguish between small- and large-size avalanches. We find that brain regions with higher white matter node degree connectivity are more likely to be active during small avalanches, whereas less connected regions require higher levels of activity to be recruited. This suggests that the underlying structural connectivity plays a role in shaping the temporal and spatial organization of avalanche dynamics.

Quantifying the ergotropy (a.k.a. available energy), namely the maximal amount of energy that can be extracted from a thermally isolated system, is a central problem in quantum thermodynamics. Notably, the same problem has been long studied for classical systems as well, e.g. in plasma physics and astrophysics, where the basic principles for its solution are known for the case of collisionless fluids. Here we provide the general analytical expression of ergotropy of classical systems valid regardless of their size and the type of interparticle interactions, and show that it emerges as the classical limit of the quantum expression of ergotropy, for quantum systems that are classically ergodic. We thus establish a unified theory of classical and quantum ergotropy, whose applicability ranges from atomic to galactic scale. www.doi.org/10.1209/0295-5075/ae652c

La caratterizzazione dell'entanglement in sistemi multipartiti ad alta dimensionalità rappresenta una sfida cruciale nell'ambito dell'informazione quantistica. In questo contributo si discute l'Entanglement Distance, una misura di correlazione quantistica basata sulla geometria dello spazio di Hilbert, analiticamente trattabile per stati puri arbitrari. Sfruttando la sua invarianza rispetto alla dimensionalità delle partizioni, l'Entanglement Distance viene impiegata per calcolare analiticamente il valore medio di entanglement per un ensemble di stati generati casualmente secondo la misura di Haar. Partendo da questi risultati esatti, si introduce un algoritmo variazionale mirato alla ricerca di stati quasi Assolutamente Massimamente Entangled (AME) per sistemi di dimensione arbitraria. Oltre a esibire proprietà di correlazione statisticamente superiori rispetto ai tipici Haar random states, gli stati ottimizzati ottenuti tramite questo approccio presentano una spiccata sparsità (ovvero un numero ridotto di componenti e ampiezze di probabilità non nulle nella base computazionale). Quest'ultima caratteristica teorica si traduce in un vantaggio tecnologico cruciale, poiché ne facilita significativamente la preparazione e l'implementazione su hardware quantistici reali, riducendo la complessità dei circuiti di controllo.

Flagella and cilia play a crucial role in microscale fluid dynamics, powering the motion of cells and driving flows in biological systems. In this talk, we present a theoretical framework to understand how semiflexible filaments respond to traveling-wave perturbations that mimic the action of molecular motors. By modeling the flagellum as a worm-like chain (WLC), we explore the competition between active forcing and intrinsic bending rigidity, revealing how this interplay selects spatiotemporal beating patterns akin to those observed in sperm tails, Chlamydomonas cilia, and eukaryotic flagella in general. Through a systematic analysis of the WLC's response, we identify the key physical parameters that shape flagellar motion and discuss their implications for biological propulsion and artificial microswimmers. Our findings offer a simple mathematical interpretation of the fundamental elements governing active filament dynamics in complex fluid environments.

Hierarchical modularity is a ubiquitous feature of complex systems, from biological and neural networks to social and technological infrastructures, yet the general physical principle underlying its emergence remains unclear. Here we show that hierarchical interactions can arise as the optimal architecture for multiscale information processing in sparse interconnected systems. Using the network density matrix formalism, we define a scale-dependent thermodynamic efficiency that quantifies the trade-off between information transport, dynamical trapping, and response diversity across propagation scales. We then introduce an integrated efficiency, obtained by aggregating this quantity over all scales, as a macroscopic variational principle for network organization. Analytical arguments and numerical experiments show that hierarchical modular architectures maximize integrated efficiency. Therefore, such architectures are not merely a descriptive hallmark of complexity, but the emergent outcome of a general information-thermodynamic optimization principle governing multiscale dynamics in complex systems.

In recent years, machine learning has achieved remarkable success, yet many of its models remain difficult to interpret. In this talk, I present an alternative perspective in which learning is formulated in terms of dynamical systems with explicitly designed attractors. Within this framework, data are treated as initial conditions of a continuous-time evolution, and classification emerges from the asymptotic state reached by the system. Each class is associated with a stable attractor, and learning amounts to shaping the interactions so that trajectories converge to the appropriate equilibrium. Moreover, the introduction of stochasticity transforms deterministic attractors into probability distributions, providing a direct link to generative modeling. The same dynamical system can therefore be used not only to classify data, but also to generate new samples by exploiting the structure of the learned attractors. This framework offers a transparent and physically grounded interpretation of learning processes, where information is encoded in the geometry of the dynamical landscape. I will discuss recent results and outline how this perspective may contribute to bridging machine learning and theoretical physics.

Collective turns in starling flocks propagate linearly with negligible attenuation, indicating the existence of an underdamped sector in the dispersion relation. Beside granting linear propagation of the phase perturbations, the real part of the frequency should also yield a spin-wave form of the unperturbed correlation function. However, new high-resolution experiments on real flocks show that underdamped traveling waves coexist with an overdamped Lorentzian correlation. Theory and experiments are reconciled once we add to the dynamics a Fermi-Pasta-Ulam-Tsingou term.

G. Consolini (1), E. Papini (1) and R. Benzi (2) 1) INAF-Istituto di Astrofisica e Planetologia Spaziali, Roma, Italy 2) Dip. Di Fisica, Univ. Roma Tor Vergata, Roma, Italy The Bolgiano-Obukhov (BO) theory of buoyancy-driven turbulence has remained without clear experimental confirmation in any real natural system for over six decades. Here, we report a possible first observational evidence of BO scaling obtained from electric field fluctuations measured inside equatorial ionospheric plasma bubbles by the CSES-01 satellite, used as a proxy for the underlying plasma velocity field. Analysing the second-order structure function across three independent events, we identify a well-defined dual turbulent regime and a characteristic scale, the Bolgiano scale L_B: below L_B, fluctuations follow Iroshnikov-Kraichnan MHD scaling consistent with Alfvénic turbulence, while above L_B the r^(6/5) power law characteristic of BO convective turbulence emerges unambiguously. The onset of BO scaling is observed in the quasi-two-dimensional geometry of plasma bubbles at late evolutionary stages, when magnetic field alignment stretches them into elongated structures with aspect ratios of order 0.01–0.04. Rescaling by L_B produces a remarkable data collapse across all three events, pointing to a universal turbulent behavior governed by the bubble geometry and revealing a quasi-exponential relation between L_B and the transverse size of the structure.

Statistical seismology classifies earthquakes into three main categories: mainshocks, foreshocks, and aftershocks. A mainshock is typically defined as the largest earthquake within a seismic sequence or region, aftershocks are the events triggered by it, and foreshocks are the earthquakes that occur before the mainshock. This definition immediately highlights a fundamental problem: unlike aftershocks, foreshocks can only be identified retrospectively, once the mainshock has already occurred. As a result, it remains unclear whether foreshocks carry genuine predictive information or simply reflect ordinary seismic clustering viewed in hindsight. The Epidemic-Type Aftershock Sequence (ETAS) model is the standard framework used to describe seismicity as a branching process in which earthquakes trigger subsequent events. Although ETAS successfully reproduces many features of aftershock clustering, it systematically underestimates the number of foreshocks observed in real seismic catalogs and does not provide a physical mechanism for earthquake nucleation. To address this limitation, we introduce the ETAS-BC model, an extension of ETAS in which earthquakes can generate magnitude-ordered chains of “connector” events that progressively activate the fault system and culminate in a mainshock. Within this framework, foreshocks emerge as the manifestation of a preparatory process rather than as a purely retrospective classification. The model remains analytically tractable, allowing us to derive predictions for the magnitude distribution, productivity, and spatio-temporal organization of connector sequences. Comparison with Southern California seismicity shows that ETAS-BC reproduces the observed number of foreshocks significantly better than standard ETAS while preserving its successful description of aftershock statistics. These results suggest that introducing connector-driven nucleation processes provides a promising physics-based framework for describing earthquake preparation and improving statistical models of seismicity.

We introduce a single-qubit quantum measurement engine powered by backaction energy input. This engine utilizes the fundamental principles of quantum measurement and feedback to harness work from the system. To reduce the energetic costs associated with information processing, we propose a lazy feedback mechanism. The lazy feedback step stochastically utilizes measurement outcomes, prescribed by a designated laziness probability. As a result, the cumulative work extracted over successive cycles of the engine exhibits a second-order Markov process, analogous to a classical run-and-tumble process with transient anomalous diffusion. We derive exact analytical expressions for finite-time moments of the extracted work and key statistical measures, including first-passage-time distributions. Furthermore, we obtain the optimal laziness probability that maximizes the mean power extracted per cycle from the quantum engine. All analytical results on the extracted work are readily applicable to the run-and- tumble process, for which obtaining first-passage-time distributions is highly nontrivial. Our work thus highlights hitherto-unexplored links between quantum engine and active matter.

Experimental evidence suggests that the healthy brain operates near a critical regime, characterized by scale-free neuronal avalanches. Recent research has increasingly focused on the mean temporal profiles of neuronal avalanches, as a more stringent and reliable test for criticality. Scaling arguments predict that, when appropriately rescaled, the mean temporal profiles of avalanches of widely varying durations should collapse onto a single scaling function, often approximated by an inverted parabola. Experimental measurements have revealed clear departures from perfect symmetry, often displaying leftward skewing and extended tails. We have investigated the stochastic Wilson–Cowan model on a modular network, in which synaptic strengths differ between intra-module and inter-module connections. The system exhibits a rich phase diagram, comprising symmetric and "broken symmetry" phases. We found that, at the edge of the transition to a symmetric phase, avalanches are right-ward skewed, as observed also in the non-modular Wilson–Cowan model. On the other hand, at the transition to a "broken symmetry" phase, avalanches become left-ward skewed. We found that in the latter case avalanches proceed in two stages: an initially cooperative regime, where excitatory activity is prevalent, followed by inhibitory competition that selects one dominant module and suppresses the others. This is the relevant mechanism leading to a fast rise of the avalanche, followed by a slower decay, and therefore to leftward asymmetry. These findings contribute to a better understanding of the relationship between brain network topology and functional brain activity.

Finding a target in a complex environment is a fundamental challenge across natural systems, from chemical reactions to sperm cells reaching an egg. One powerful strategy to reduce search times is redundancy: deploying multiple independent searchers increases the probability of success, particularly when this is driven by rare events. When the underlying stochastic motion features broadly distributed step lengths, rare long relocations dominate the dynamics, making redundancy especially effective. In this work, we investigate the statistics of extreme events for the mean first passage time in a system of $N$ independent walkers performing power-law-distributed jumps with finite velocity $v$, where target-reaching events are governed by single large fluctuations. We show that the mean first passage time of the fastest walker scales as $1/N$, representing a dramatic speed-up compared to classical Brownian motion, and saturates at the minimum value $X/v$. The model is further extended to include random velocities. For a fixed $N$, we identify a crossover governed by a critical tail exponent $\alpha_c$, which separates a regime dominated by a single large fluctuation ("big jump") from a regime characterized by Gaussian extreme-value statistics arising from finite sampling effects. From these results, a scaling law linking the number of searchers $N$ to the size $X$ of the search region is derived. Ultimately, these findings demonstrate how redundancy, combined with rare-event statistics, can efficiently organize target-search processes in complex biological environments. As a prototypical application, we consider mammalian fertilization, deriving a cross-species scaling relation between the number of spermatozoa and the typical uterine size within a coarse-grained description.

Phase-separation of chimeric proteins resulting from genetic mutations has been shown to trigger aberrant chromatin looping, contributing to disease development, including cancer [1]. However, the physical mechanisms regulating these processes remain unclear. In this study, we employ polymer physics models of chromatin [2] to investigate the relationship between protein self-aggregation and chromatin structure [2]. We show that a simple model, including only protein-protein and protein-chromatin interactions, effectively explains the aberrant looping around certain oncogenes in cells expressing the NUP98-HOXA9 chimera [1], commonly found in leukemia. Moreover, when incorporating the presence of cohesin in a more complex model [3], similar results are observed, suggesting a weak dependence of these looping mechanisms on loop-extrusion. Finally, leveraging our molecular dynamics simulations, we compare our findings with experimental data [1] and show that phase-separation properties of the chimera can be harnessed to prevent enhancer-gene contacts, thereby offering a potential strategy for cancer prevention [3]. [1] J. H. Ahn et al., “Phase separation drives aberrant chromatin looping and cancer development”. Nature 595, 591-595 (2021). [2] A. M. Chiariello, F. Corberi, M. Salerno, “The Interplay between Phase Separation and Gene-Enhancer Communication: A Theoretical Study”. Biophys. J. 119, 873-883 (2020). [3] Guha, Fontana et al., “Loop-extrusion and polymer phase-separation can co-exist at the single-molecule level to shape chromatin folding”. bioRxiv (2025).

We present the Renormalized Dual Basis (RDB), a scalable and resource-efficient framework for the classical and quantum simulation of lattice gauge theories (LGTs) with continuous gauge groups in higher dimensions. The method combines a dual formulation of the theory with a local optimization of the gauge basis, obtained from the solution of the single-plaquette problem, enabling an efficient truncation of the infinite-dimensional Hilbert space of gauge degrees of freedom. We apply the approach to both Abelian and non-Abelian LGTs in two spatial dimensions, focusing on compact quantum electrodynamics (cQED) and pure SU(2) gauge theories. For small lattices with periodic boundary conditions in the pure gauge case, and open boundary conditions in the presence of fermionic matter, we determine the ground state properties of the theory and compute gauge-invariant observables such as the plaquette expectation value. Compared to standard truncation schemes, the RDB achieves improved accuracy while requiring significantly fewer local basis states across all coupling regimes. To assess the scalability of the method, we further investigate larger lattice systems using tensor network algorithms. These results demonstrate that the RDB remains efficient as the system size increases, without a dramatic growth in computational resources.

Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, τeq~ Vˆ1.0. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to≃ 1.1 × 10ˆ9 monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to N ≃ 5 × 10ˆ5 monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as Nˆ1/4.

Engineered systems with antagonistic interactions remain comparatively unexplored, particularly because their emergent phases are closely linked with frustration mechanisms in the hosting network. In this context, the spin glass theory has shown how an apparently uncontrollable non-ergodic chaotic behavior arises from the complex interplay of competing interactions and frustration among units, leading to multiple metastable states preventing the system from exploring all accessible configurations over time. Here, we show how topology constrains dynamics in systems with antagonistic interactions. We make use of the signed Laplacian operator to demonstrate how fundamental topological defects in lattices and networks percolate, shaping the geometrical arena and complex energy landscape of the system. This unveils novel, highly robust multistable phases and establishes deep connections with spin glasses when thermal noise is considered, providing a natural topological and algebraic description of emergent multistability and non-ergodicity in frustrated systems.

The formation of polarized signaling domains on cell membranes is a fundamental example of biological pattern formation. While such patterns resemble structures from equilibrium phase separation, they are intrinsically non-equilibrium, driven by energy-consuming enzymatic cycles that switch molecules like phosphoinositides or small GTPases between distinct states. We develop a minimal model of this enzyme-driven phase ordering process. Starting from microscopic reaction kinetics, we derive a mesoscopic theory that belongs to the class of active Model A with a global constraint. This framework yields an explicit mean-field phase diagram and closed-form expressions for key observables, such as interfacial tension, domain fractions, and phase coexistence boundaries, in terms of kinetic rates. In this context, phase coexistence is controlled by non-equilibrium parameters like catalytic rates and enzymatic asymmetry, rather than equilibrium parameters such as saturation concentrations. The resulting phase-separated domains rapidly exchange material with their surroundings. Their maintenance requires a continuous power input determined by enzymatic kinetics. The predicted phenomenology is consistent with experimental observations on reconstituted systems of phosphoinositide and Rab5 membrane patterning. We further study how metastable uniform states decay via nucleation of minority-phase domains and subsequent coarsening, driven by an effective interfacial tension. Using large deviation theory, we derive the critical nucleation radius under the action of the intrinsic, multiplicative chemical noise. The analytical results are quantitatively confirmed by stochastic simulations of a lattice-gas implementation of the process. Our work provides a theoretical framework identifying key biochemical parameters controlling active phase separation on membrane scaffolds, offering testable predictions for experiments. References https://arxiv.org/abs/2512.08356

Many real-world infrastructures, from sensor and road networks to power grids, are spatially embedded and anisotropic, with constraints on the maximum number of links each node can establish. Such systems can be represented as anisotropic limited-degree networks, in which each node forms at most q outgoing links preferentially oriented along a fixed direction. By increasing the node density σ at fixed q, we uncover a reentrant percolation transition: a giant strongly connected component emerges, but unexpectedly disintegrates again at high densities. This counterintuitive behavior implies that adding nodes, normally expected to enhance robustness, can instead reduce mutual accessibility and weaken global connectivity. The critical behavior displays two coexisting “faces”: random-percolation scaling along the preferred direction and directed-percolation scaling transversely, therefore we name this phenomenon Janus percolation, in analogy with the dual-faced Roman god. These findings demonstrate that anisotropy and degree limitation can jointly induce a novel reentrant connectivity with mixed universality that bridges the universality classes of random and directed percolation, providing fresh insight into how structural constraints shape connectivity and resilience in spatial networks.

The quantum $O(n)$ model has long served as a valuable framework for studying both equilibrium and dynamical properties of quantum many-body systems. In this talk, we investigate its non-equilibrium dynamics following a quantum quench in the large-$n$ limit. While the model is known to be tractable in this regime, we show that it is in fact integrable - with integrals of motions stemming from that of the classical Neumann model - thus enabling a complete analytical solution of its dynamics. This integrability reveals a synchronization mechanism that gives rise to persistent oscillations, interpretable as Higgs modes localized at the edge of the spectral band. We further demonstrate that the long-time behavior is governed by a Generalized Gibbs Ensemble (GGE), in contrast to previous expectations, and we obtain exact critical exponents differing from those commonly reported. Remarkably, integrability persists even in the presence of long-range couplings, allowing us to explore the crossover between mean-field and genuinely many-body regimes in terms of parametric Floquet resonances of the microscopic degrees of freedom.

We investigate the thermodynamic and non-equilibrium properties of an open nonlinear diamond lattice under the influence of a uniform magnetic field. The chain exhibits two dispersive bands and one zero-energy flat band. By fine-tuning the magnetic flux, all three Bloch bands turn flat, resulting in Aharonov-Bohm caging and the total suppression of particle and energy currents. The equilibrium phase diagram is obtained as function of the flux. By driving the system at the boundaries with two thermostats, we study the transport of norm and energy across the system for different flux values and nonlinear strengths. For weak nonlinearity, the caging condition turns the system into an insulator, while the system is ''metallic'' for all other flux values. For intermediate nonlinear strength instead, the system behaves as a conductor for any flux value. However, in this regime the caging condition enhances Seebeck coefficient and the figure of merit, improving the thermoelectric features of the chain. These results highlight the magnetic flux as a versatile control parameter for effectively tuning the thermodynamic and transport signatures of the system.

We employ molecular dynamics (MD) simulations to determine how magnesium perchlorate (Mg(ClO4)2) and calcium perchlorate (Ca(ClO4)2) alter the phase diagram, structure, and dy- namics of supercooled TIP4P/2005 water. We focus on the interplay between its low-density (LDL) and high-density liquid (HDL) phases and the glassy dynamics, simulating solutions at concentrations from low to moderate. Thermodynamic analysis confirms the persistence of water anomalies, albeit shifted by the solutes. A second-order liquid-liquid critical point (LLCP) was located at low concentrations, but not at moderate concentrations within the simulated temperature range. Dynamically, similar to the bulk, water in these solutions follows the Mode Coupling Theory, exhibiting a fragile-to-strong crossover. Structurally, radial distribution functions demonstrate that increasing solute concentration enhances HDL-like behaviours and suppresses LDL ordering, the nucleation being favoured in LDL water. This correlates with a marked contraction of the LDL-like region in the (p, T) phase diagram, inferred from compressibility maxima shifts, which serve as a proxy for the maxima of the HDL-LDL correlation length. In light of recent potential radar evidence for aqueous solutions of perchlorates approximately 1.5 km underneath Mars’ south pole, it is of importance to assess their low-temperature stability and the possible crucial role of water anomalies in this context.

We introduce, develop, and investigate a connection between multiphoton quantum interference, a core element of emerging photonic quantum technologies, and Hopfield-like Hamiltonians of classical neural networks. Combining a system composed of indistinguishable photons in superposition over a set of field modes, a controlled array binary phase-shifters, and a linear-optical interferometer, we can show that the output photon statistics can be described by means of a p-body Hopfield Hamiltonian. We exemplify the analysis of the generalized 4-body Hopfield model obtained through this procedure and show that it realizes a transition from a memory retrieval to a memory black-out regime, i.e. a spin-glass phase, as the amount of stored memory increases. The mapping enables novel routes to the realization and investigation of disordered and complex classical systems via photonic quantum simulators, as well as the description of aspects of structured photonic systems in terms of classical spin Hamiltonians.

We study the memorization and generalization capabilities of a generative diffusion model in the case of structured data defined on a latent manifold. We specifically consider a set of P data points in N dimensions lying on a latent subspace of dimension D, according to the hidden manifold model. Our analysis considers a generative reverse process given by the empirical score function as a proxy of the true one, and then precisely characterizes the process in the high-dimensional limit, by exploiting a connection with the random energy model (REM). We provide evidence for the existence of an onset time, when traps appear in the time-varying potential, although they do not affect typical trajectories. The size of the basins of attraction of such traps is computed at any time. Moreover, we derive the collapse time, at which trajectories fall in the basin of one of the training points, implying memorization. We show that the curse of dimensionality issue is mitigated for highly structured data, i.e. the relevant dimension governing the time at which memorization happens is the intrinsic dimension D instead of the ambient dimension N. .

We investigate the statistical properties of mafia-related homicidal events occurred in the city of Palermo (Italy) from 1950 to 2020. Such data are extracted from a unique electronic archive containing microdata on mafia-related homicides, attempted homicides and disappearances committed in Sicily. This electronic archive is maintained by the Palermo Prosecutor’s Office (Direzione Distrettuale Antimafia) and is regularly consulted by magistrates investigating crimes associated with Cosa Nostra. Specifically, we aim to understand how geolocalizing homicides within the greater Palermo area can assist researchers and law enforcement authorities (Judiciary and Law Enforcement Agencies) in better characterizing and potentially pre- dicting the temporal (micro-)patterns of crimes perpetrated by Cosa Nostra syndicates. To this end, we combine homicidal microdata with population density data at the submunicipal level of neighbourhoods (quartieri). This integration allows us to identify areas where the incidence of homicides is significantly higher or lower than expected under a null hypothesis of random distribution, adjusted for the actual population density in Palermo. In this way, we highlight neighbourhoods disproportionately affected by homicidal events, not in absolute terms, but rel- ative to local population figures during a certain time period. The time periods we are considering are obtained by using an unsupervised statistical procedure that is able to highlight the temporal points when the statistical properties of the homicidal time series changes its statistical properties. The underlying idea is that such changes are associated to a regime shift in the Cosa Nostra criminal activities. The analyses presented in this paper may be usefully employed, at the very least, to reconstruct the broader context in which homicides occur.

Biochemical reactions in living systems are affected by macromolecular crowding, a phenomenon attributed to excluded volume effects and nonspecific interactions, yet these reactions are usually studied in dilute solutions. Here, we investigate crowding effects on the activity of some key enzymes found in the extracellular matrix (ECM), such as elastase and collagenase, using controlled solutions of the branched polymer dextran. Dextran solutions are characterized via rheology and diffusion measurements. Polymer transport properties exhibit scaling-invariant behavior governed by degree of polymerization and branching, whereas water diffusivity and solution density do not depend on the degree of polymerization. These results enable the construction of volume fractions tailored to the physical observable of interest. The enzymatic activity of ECM proteases is quantified through spectrophotometric assays. We introduce a theoretical framework for fluorescence detection in non-ideal mixtures and apply it to the full progress curve assays of key ECM enzymes. For elastase, the degradation of a peptide is enhanced by crowding and reveals an equilibrium constant exhibiting the same scaling behavior as dextran transport properties, suggesting polymer size and topology as tunable parameters in crowding experiments.

Understanding heat transport in insulating solids at low temperature poses a fundamental challenge in statistical physics, where classical approaches based on Green–Kubo (GK) theory and molecular dynamics fail to capture quantum effects, while semi-classical corrections remain inherently perturbative. Here, we revisit thermal conductivity from a unifying statistical-mechanical perspective, contrasting three levels of description: (i) classical GK calculations, (ii) classical dynamics supplemented by quantum statistical weights (e.g. quantum specific heat corrections), and (iii) fully quantum formulations based on many-body equilibrium correlations. Building on the framework introduced in [1], we present a non-perturbative approach combining Path Integral Monte Carlo (PIMC) simulations with linear-response theory. Within this formulation, transport coefficients are expressed in terms of imaginary-time current–current correlation functions, which encode the full quantum statistics of the system. The central technical challenge, recovering real-time transport from imaginary-time data, is addressed via controlled analytical continuation, guided by physically motivated priors for the spectral density. This approach allows us to go beyond the standard Peierls–Boltzmann and quasi-harmonic GK pictures, which rely on phonon lifetimes and fail to describe the low-temperature increase of thermal conductivity. Instead, we demonstrate the emergence of a distinct transport lifetime, directly extracted from current correlations, highlighting the breakdown of single-particle (phonon) descriptions of heat transport. The methodology provides a consistent statistical-mechanical framework in which equilibrium quantum fluctuations, encoded in imaginary time, determine dynamical transport properties. More broadly, this work illustrates how modern quantum Monte Carlo methods, combined with spectral reconstruction techniques, enable a fully microscopic and non-perturbative treatment of transport in condensed matter systems, opening the way to quantitative studies of heat conduction in regimes where both anharmonicity and quantum statistics are essential. [1] Vladislav Efremkin, Stefano Mossa, Jean-Louis Barrat, Markus Holzmann, "Computation of thermal conductivity based on Path Integral Monte Carlo methods", arXiv:2602.16405

Finding a target in a complex environment is a fundamental challenge across natural systems, from chemical reactions to sperm cells reaching an egg. One powerful strategy to reduce search times is redundancy: deploying multiple independent searchers increases the probability of success, particularly when this is driven by rare events. When the underlying stochastic motion features broadly distributed step lengths, rare long relocations dominate the dynamics, making redundancy especially effective. In this work, we investigate the statistics of extreme events for the mean first passage time in a system of $N$ independent walkers performing power-law-distributed jumps with finite velocity $v$, where target-reaching events are governed by single large fluctuations. We show that the mean first passage time of the fastest walker scales as $1/N$, representing a dramatic speed-up compared to classical Brownian motion, and saturates at the minimum value $X/v$. The model is further extended to include random velocities. For a fixed $N$, we identify a crossover governed by a critical tail exponent $\alpha_c$, which separates a regime dominated by a single large fluctuation ("big jump") from a regime characterized by Gaussian extreme-value statistics arising from finite sampling effects. From these results, a scaling law linking the number of searchers $N$ to the size $X$ of the search region is derived. Ultimately, these findings demonstrate how redundancy, combined with rare-event statistics, can efficiently organize target-search processes in complex biological environments. As a prototypical application, we consider mammalian fertilization, deriving a cross-species scaling relation between the number of spermatozoa and the typical uterine size within a coarse-grained description.

Long-range coherence is a defining property of written language, persisting across entire books through stable statistical scaling and structured information flow. We show that this property is organized along two nearly orthogonal directions of variability. In this multivariate space, the mean representation of natural books follows a smooth trajectory parameterized by text length. Using a contemporary LLM with an iterative self-conditioning protocol, we generate long texts that converge toward stable coherence regimes and occupy regions of descriptor space comparable to those of human-written books at similar lengths. Under highly stochastic generation, statistical scaling descriptors remain within natural-text ranges, whereas informational descriptors systematically deviate, indicating a differential robustness across coherence measures. These results show that contemporary autoregressive language models can reproduce key large-scale statistical structures of written language, while revealing distinct stability regimes governing different aspects of coherence under chaotic generation.

In this work, we investigate the functional controllability of a well-known model of collective behavior: the Ant Swarm Model. We introduce a population of controlling agents, trained via Reinforcement Learning (RL), to influence the dynamics of the system and promote the emergence of ordered behavior. Smart-agents are optimized with Proximal Policy Optimization in a centralized-training decentralized-execution setting, and interact with ants only through the shared pheromone field. The reward design promotes trail pheromone structures and alignment of ant positions with high-pheromone paths, without requiring control of specific microscopic configurations. Our results demonstrate that the learned policies effectively shift the phase transition line that characterizes the global behavior of the system, enabling the formation of organized trails in regimes that are typically dominated by randomness. Compared with both the baseline system and an enhanced-hybrid setup, with equal pheromone reinforcement but no learned policy, our approach yields consistently higher ordering and quality metrics across the phase diagram. This study provides insights into the potential of RL based control strategies for stigmergic systems and contributes to the general understanding of functional controllability in complex systems.

We investigate how long-range interactions affect consensus formation in a one-dimensional voter model for opinion dynamics. Agents hold binary opinions and update them through a competition between local nearest-neighbor interactions and long-range social links, whose strength decreases with distance. We show that even a small amount of nonlocal interaction can strongly modify the coarsening process, leading to consensus. Depending on how rapidly long-range links decay, the system displays different collective behaviors: a short-range-like regime with a growing crossover scale, a long-range-dominated regime with modified domain growth, and a regime where complete coarsening is suppressed and the system reaches a stationary state. These results show how sparse nonlocal connections can reshape collective decision-making in social and complex systems.

We investigate the role of contact interactions in the dynamics of fuzzy dark matter (FDM), modeled through the Schrödinger–Poisson equation. While the $\Lambda$CDM paradigm successfully expl$

Describing the dynamics of quantum many-body systems is a formidable problem in contemporary physics. Understanding these dynamics is crucial for characterizing non-equilibrium phenomena and for the development of quantum technologies. The simulation of such systems with variational methods is a promising yet challenging task, especially in regimes where highly expressive ansätze lead to numerical instabilities. We introduce an extension of the time-dependent variational Monte Carlo (tVMC) method [1] that adaptively controls the expressivity of the variational quantum state during the dynamics. Our adaptive tVMC (atVMC) [2] approach addresses the ill-conditioned equations of motion arising in overparameterized regimes by selectively evolving only the most relevant parameters at each time step. Relevance is quantified through the local-in-time error (LITE), which measures the deviation between variational and exact evolution, using only quantities already available in standard tVMC simulations. We benchmark the method on quantum quenches in the one-dimensional transverse-field Ising model using both spin-Jastrow and restricted Boltzmann machine wave functions. The adaptive scheme significantly improves numerical stability and reduces the need for strong regularization, enabling reliable simulations with highly expressive variational ansätze. [1] G. Carleo, F. Becca, M. Schiró, and M. Fabrizio, Sci. Rep. 2, 243 (2012). [2] R. Salioni, R. Martinazzo, D.E. Galli, C. Apostoli, Phys. Rev. B 113, 014408 (2026).

The realisation of Bose-Einstein condensation of photons under grand-canonical conditions has provided experimental evidence for the simultaneous occurrence of macroscopic fluctuations and phase coherence of the condensate. The observation of these two features, against a consolidated tradition which wants the fluctuations to be pathological (grand-canonical catastrophe) and incompatible with spontaneous symmetry breaking, calls for a comprehensive rethinking of the approach to the problem. In this talk we consider the uniform ideal gas in a box and we present an alternative conceptual framework. We show that the usually-employed Bogoliubov quasi-average construction fails to reproduce the broken-symmetry state. The observed features are accounted for by a different pattern of spontaneous symmetry breaking, characterized by condensation of fluctuations and long-range correlations of the order parameter.

Recently, it was shown that quantum interference in a system containing a polarized and an unpolarized emitter can allow directional emission of photons into a circulating cavity. Here we ask whether high directionality of photon emission in this system implies a high degree of quantum correlation between the two emitters. We show that the answer is a qualified “yes,” with photon emission directionality and emitter-emitter entanglement showing a monotonic relationship over a broad parameter range. The relationship breaks down only in the limit of perfect directionality. Furthermore, under reasonable assumptions for experimental parameters and stability, we show that the statistics of measured directionality allow a reliable estimate of the concurrence. This result implies that directionality of photon emission in the state preparation stage can be used to determine the entanglement between the emitters, with potential applications to more generic cases including quantum networks.

Phase separation underlies a broad range of phenomena, from materials science to biological organization, and is commonly characterized by the emergence of universal power laws t^z governing domain-growth evolution. In the present contribution, we present our recent results concerning the investigation of a phase-separating polar active model comprising a scalar density field with an advective coupling to a polarization field, the latter modeling self-propulsion. Our analysis reveals a novel growth regime with exponent z∼0.6, significantly faster than the typical z∼1/3 behavior of conserved systems, and in quantitative agreement with the accelerated growth recently observed in extensive simulations of polar active particles. Combining numerical simulations in two and three dimensions with analytical arguments, we identify the mechanism underlying this accelerated coarsening: self-propulsion facilitates the creation of topological defects and compresses dense domains, thus leading to faster growth. We further demonstrate that the accelerated-growth regime is robust against several model extensions, including additional self-advection of the polarization field and non-equilibrium contributions inspired by well-established field-theoretic models. Overall, our results provide a minimal field-theoretical framework that explains recent observations of polar active particles, opening new perspectives for understanding living systems and designing active materials.

We study the ordering kinetics of a one-dimensional generalization of the voter model with long-range, power-law interactions, the $p$-voter model. In this model, the agent, or spin, located at a site of a lattice adopts the majority state among $p$ other agents, whose distances $r$ are drawn from a probability distribution $P(r) \propto r^{-\alpha}$. For $p=2$, the model can be mapped onto the voter model with the same long-range interactions. For $3 \leq p < \infty$, the dynamics belongs to the universality class of the one-dimensional Ising model with long-range coupling $J(r)=P(r)$, quenched to small but finite temperatures. In the limit $p \to \infty$, we observe a crossover to the distinct behavior of the long-range Ising model quenched to zero temperature.

Marine microbes sustain Earth’s major biogeochemical cycles, yet how they maintain stable ecosystem functions across diverse environments remains unclear. We analyzed metagenomic and metatranscriptomic data from diatom communities sampled during the Tara Oceans global expedition. While gene abundance distributions remain statistically similar across samples, gene expression varies systematically across geographical locations. We show that this global pattern reflects predictable scaling laws \new{that link stable gene abundance reservoir} to functional responses. Global distributions, scaling relationships, and variability among sampling stations are captured by a stochastic model linking gene abundance dynamics to gene expression, which depends on the efficiency of transcription relative to degradation. While colder waters promote higher transcriptional activity and warmer regions show more selective gene usage, we find that transcript abundance increases nonlinearly with unigene richness. This general scaling is captured by our model and suggests that diatom communities balance high expression of core genes with specific functional diversity. These scaling relationships hold consistently across ocean basins, requiring only temperature to predict transcriptional patterns from genetic composition. Our findings reveal how \new{the stability of gene abundance structure in diatoms} ecosystems coexists with transcriptional variability, enabling flexible functional responses.

Real ecological communities are characterized by sparse interaction networks, while most analytical results rely on fully connected models. In this work, we investigate how network sparsity shapes ecological communities within a generalized Lotka–Volterra framework with random interactions and demographic noise. Using methods from statistical physics, in particular the cavity method and Belief Propagation, we obtain an exact characterization of equilibrium properties on sparse networks. We show that sparsity alone induces strong deviations from Gaussianity in species abundance distributions, even when interactions are Gaussian and the system is in a single-equilibrium phase. In particular, abundance distributions become Gamma-like, in agreement with empirical observations. In addition, we uncover a novel topological multiple-equilibria phase, fundamentally different from that of fully connected models. In this phase, multiple attractors emerge due to extinction-driven fragmentation of the interaction network. These results highlight network sparsity as a key ingredient for realistic ecological modeling and provide new insight into the structure and stability of complex ecosystems.

The scaling limit where both the size of the training set $P$ and the width $N$ of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks. However, extending these non-perturbative results from shallow architectures to deep non-linear networks has proven very challenging. Here we present a surprisingly effective approximate approach to predict the generalization performance of Bayesian multi-layer perceptrons (MLPs) and of fixed depth $L$ on arbitrary high-dimensional data. We propose an "equivalent Wishart Ansatz" to capture the dominant stochastic fluctuations of the hierarchical empirical kernels of MLPs. This allows us to perform a large deviation analysis for the partition function of MLPs in the proportional limit, expressed in terms of a renormalized NNGP kernel. In this description, even strong representation learning in the proportional limit is encoded in at most $L$ scalar order parameters, determined self-consistently. Extending the approach to convolutional architectures (CNNs), we identify a hierarchical local kernel renormalization mechanism, which allows to quantify more complex data-dependent transformations of the large-width kernel in CNNs due to finite-width effects. We test our effective theory against sampling experiments from the Bayesian posterior of finite deep neural networks with depths $L \sim O(10)$ and $P\sim O(10^3)$ on classic benchmark datasets, finding overall very good agreement together with two distinct types of systematic deviations.