Riccardo Aiudi  Unipr  INFN
Predicting the effect of training on the internal representations of finitewidth Bayesian onehidden layer networks
In this work, we compute analytically the effect of training on the internalrepresentations of a Bayesian onehidden layer neural network at finitewidth,using the theoretical framework introduced in [1]. In particular, we investigatehow the kernel matrix related to these internal representations changes aftertraining. We observe that the kernel matrix elements differ from the infinitewidth ones by terms of order O(1/N) and we precisely compute this correction.We perform numerical experiments to validate our predictions using Gaussiandata, both with random labels and in a teacherstudent setting and we presentpreliminary experiments with regression tasks from the CIFAR10datasets.
[1] S Ariosto, R Pacelli, M Pastore, F Ginelli, M Gherardi, and P Rotondo.Statistical mechanics of deep learning beyond the infinitewidth limit. arXivpreprint arXiv:2209.04882, 2022. 
Hanieh Alvankar Golpayegan  University of naples Federico II
Bistability and criticality in the stochastic WilsonCowan model
We study the stochastic version of the WilsonCowan model of neural dynamics, where the response function of neurons grows faster than linearly above the threshold, representing a cooperative effect of different synaptic inputs. The model shows a region of parameters where two attractive fixed points of the dynamics exist simultaneously, corresponding to lower and higher activity, and the dynamics switches between them as observed in up and down states of cortical neurons. Along with alternation of states, the model displays a bimodal distribution of the avalanches of activity, with a power law behavior corresponding to the state of low activity, and a bump of very large avalanches due to the high activity state. The bistability is due to the presence of a first order (discontinuous) transition in the phase diagram, and the observed critical behavior is connected with the line where the low activity state becomes unstable (spinodal line). 
Sebastiano Ariosto  Università dell'Insubria
A Statistical Mechanics framework for deep neural networks beyond the infinitewidth limit.
Decadeslong literature testifies to the success of statistical mechanics at clarifying fundamental aspects of deep learning.Yet the ultimate goal remains elusive: we lack a complete theoretical framework to predict practically relevant scores, such as the train and test accuracy, from knowledge of the training data.Huge simplifications arise in the infinitewidth limit, where the number of units N_l in each hidden layer (l=1,..., L, being L the finite depth of the network) far exceeds the number P of training examples.This idealisation, however, blatantly departs from the reality of deep learning practice, where training sets are larger than the widths of the networks. Here, we show one way to overcome these limitations.The partition function for fullyconnected architectures, which encodes information about the trained models, can be evaluated analytically with the toolset of statistical mechanics.The computation holds in the ''thermodynamic limit'' where both N_l and P are large and their ratio alpha_l = P/N_l, which vanishes in the infinitewidth limit, is now finite and generic.This advance allows us to obtain(i) a closed formula for the generalisation error associated to a regression task in a onehidden layer network with finite alpha_1;(ii) an approximate expression of the partition function for deep architectures (technically, via an ''effective action'' that depends on a finite number of ''order parameters'');(iii) a link between deep neural networks in the proportional asymptotic limit and Student's t processes;(iv) a simple criterion to predict whether finitewidth networks (with ReLU activation) achieve better test accuracy than infinitewidth ones.As exemplified by these results, our theory provides a starting point to tackle the problem of generalisation in realistic regimes of deep learning. 
Michele Bellingeri  Ricercatore
Robustness and spreading properties in realworld networks
Network science offers powerful tools to model real complex systems. Here we report a comprehensive analysis of the robustness of realworld complex weighted networks to errors and attacks toward nodes and links. We use measures of the network damage conceived for a binary and a weighted network structure. We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binarytopological connectedness are almost unaffected. Complex networks are the preferential framework to model spreading dynamics in several realworld complex systems. We numerically simulated, via a typeSIR model, epidemic outbreaks spreading on 50 realworld networks, and we then tested which NSIs, among 40, could a priori better predict the disease fate. We found that the i) "average normalized node closeness" and the "average node distance" are the best predictors of the initial spreading pace, and that ii) indexes of "topological complexity" of the network, are the best predictors of both the value of the epidemic peak and the final extent of the spreading. Furthermore, commonly used NSIs are unreliable predictors of the disease spreading extent in realworld networks. 
Simone Benella  INAFIAPS
On the Langevin equation applied to weaklycollisional space plasma turbulence
In turbulence it has been widely shown that the energy transfer across different scales can be envisioned as a Langevin process. In the case of plasmas, the dynamical variables of such a Langevin process are represented by electromagnetic and velocity field fluctuations. For weaklycollisional plasmas, e.g., space plasmas, this scenario has been shown to be consistent with observations at both inertial and subion scales. One of the striking features of the turbulent dynamics at scales below typical ion lengths is the “convergence” of the statistics towards a shapeinvariant distribution of electromagnetic/velocity field fluctuations. In this work we show that in the nondiffusive limit of the Langevin equation it is then possible to derive a scaling law which presents a remarkable agreement with both satellite observations and numerical simulations of plasma turbulence. This allows us to establish a link between the Langevindrift term and the scaling exponents of subion scale fluctuations. 
Indaco Biazzo  EPFL
The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systems
Generative Autoregressive Neural Networks (ARNN) have recently demonstrated exceptional results in image and language generation tasks, contributing to the growing popularity of generative models in both scientific and commercial applications. This work presents a physical interpretation of the ARNNs by reformulating the Boltzmann distribution of binary pairwise interacting systems into autoregressive form. The resulting ARNN architecture has weights and biases of its first layer corresponding to the Hamiltonian's couplings and external fields, featuring widely used structures like the residual connections and a recurrent architecture with clear physical meanings. Moreover, its architecture's explicit formulation allows using statistical physics techniques to derive new ARNNs for specific systems. As examples, new effective ARNN architectures are derived from two wellknown meanfield systems, the CurieWeiss and SherringtonKirkpatrick models, showing superior performances in approximating the Boltzmann distributions of the corresponding physics model compared to other commonly used architectures. The connection established between the physics of the system and the neural network architecture provides a way to derive new architectures for different interacting systems and interpret existing ones from a physical perspective. 
Anna Braghetto  Università di Padova
Interpretable machine learning of amino acid patterns in proteins: a statistical ensemble approach
Explainable and interpretable unsupervised machine learning helps understand the underlying structure of data. We introduce an ensemble analysis of machine learning models to consolidate their interpretation. Its application shows that restricted Boltzmann machines compress consistently into a few bits the information stored in a sequence of five amino acids at the start or end of alphahelices or betasheets.The weights learned by the machines reveal unexpected properties of the amino acids and the secondary structure of proteins: (i) His and Thr have a negligible contribution to the amphiphilic pattern of alphahelices; (ii) there is a class of alphahelices particularly rich in Ala at their end; (iii) Pro occupies most often slots otherwise occupied by polar or charged amino acids, and its presence at the start of helices is relevant; (iv) Glu and especially Asp on one side, and Val, Leu, Iso, and Phe on the other, display the strongest tendency to mark amphiphilic patterns, i.e., extreme values of an effective hydrophobicity, though they are not the most powerful (non) hydrophobic amino acids. 
Victor Buendia  University of Tubingen and Max Planck Institute for Biological Cybernetics, Tubingen, Germany
On mesoscopic, finitesize populations of stochastic coupled oscillators
Coupled oscillators have a wide range of applications in statistical mechanics. Often, systems under study might present several scales of description. In this case, each unit of the system might be as well composed by a finite number of oscillators. However, standard meanfield theories only deal with populations in the thermodynamic limit, which lead to deterministic solutions for the order parameters. In this talk, I will introduce a novel approach to tackle this problem, which applies to any population of oscillators subject to stochastic white noise. I will apply the theory to the stochastic Kuramoto model deriving formally the multiplicative noise emerging in the mesoscopic limit, as well as finding deterministic finitesize corrections. I will show how these results allow us to derive, for the first time, almostexact closed solutions for the stochastic Kuramoto model, as well as new insights in the critical transition to synchrony. 
Lorenzo Chicchi  Università Degli Studi di Firenze
Complex and real discrete maps to automated classification
A novel model to automated classification is introduced which exploits a fully trained discrete map steer items belonging to different categories toward distinct final state. These latter are incorporated into the model by taking advantage of the spectral decomposition of the operator that rules the linear evolution across the processing network. Nonlinear terms are confined to a part of the network and allow to disentangle the data supplied as initial condition to the discrete dynamical system. The shape of the eigenvectors allows information to flow from the nonlinear part of the network to the linear part, where the output is read. The eigenvalues associated with the final states can be both real (RSN) and complex (CRSN). In the second case the final state will turn out to be a not trivial function of time. The network can be equipped with several memory kernels which can be sequentially activated for serial datasets handling. Our novel approach to classification is successfully challenged against a standard dataset for image processing training. 
Niccolò Cocciaglia  Università La Sapienza, Roma
Turbulent energy cascade seen from nonequilibrium statistical mechanics
The distinguishing feature of 3D turbulent flows is the onset of energy fluxes directed, on average, from the large forcing scale to the small dissipating one, i.e. from low to high wave numbers: a scenario called “direct energy cascade”. From a statistical mechanics point of view the cascade picture prevents the existence of detailed balance, thereby turbulent models, specifically simplified ones, are well suited to be tested and studied with the techniques of nonequilibrium statistical physics.In this talk we aim at characterizing the nonequilibrium properties of turbulent cascades in the SABRA shell model in two different ways . One is by observing how the irreversible character of the energy fluxes is revealed by a specific antisymmetric combination of timecorrelation functions. The other by showing how significantly different the relaxation behavior of an energy perturbation is, when measured at scales smaller or larger than the perturbed one. 
Giuseppe Consolini  INAFIstituto di Astrofisica e Planetologia Spaziali
Markovian features of space plasma turbulent fluctuations at subion scales
The heliosphere's space plasmas are in a turbulent state. Magnetic field fluctuations exhibit a powerlaw spectrum at large scales, or at frequencies lower than 0.1–1 Hz, with spectral exponents that are similar to those predicted by theories of fluidlike turbulence. The inertia of ions decouples from that of electrons at scales smaller than the ioninertial length, or ion/subion scales, and the spectrum of the magnetic field fluctuations exhibits a distinct dynamical regime that is yet not fully understood. By recasting the scaletoscale coupling in this domain in terms of a stochastic Langevinlike dynamics, we provide recent results on the Markovian characteristics of the fluctuations at these scales. At subion scales, a simple/global scale invariance indicates that the stochastic redistribution of energy plays a minor role. 
Sacha Cormenier  INFN Sezione Roma3
Neural Network implemented into embedded system for image recognition in particle environment and temperature study for optimization
Field Programmable Gate Arrays (FPGAs) are commonly used in physics experiments nowadays both in backend and in frontend detectors. Their endurance in radiation environment, their flexibility and their speed make them perfect candidates for experiments in high energy physics. We are exploiting a FPGA to perform image acquisition and we employ a neural network for continuous learning in a particle environment, specifically for image recognition. The purpose is to witness the physical damages and the corresponding ones inside the parameters of the network.It has been implemented using the FINN project (arXiv:1612.07119), a framework used for the implementation of neural networks on FPGAs handling optimal resource consumption. Particles interacting with cameras generate noise in the images acquired, inducing repercussions in the training and testing sessions of the network. We made a study concerning the effects of the noise with different implementations, fitting with reallife patterns, motivated by the work in arXiv:1803.08823 and we witness the corresponding consequences of such an effect in the training and testing parts.Due to the limited resources present on FPGAs, the network implemented using the FINN project incorporates a lightweight architecture. Thus, we optimize this architecture with respect to the inverse temperature criterion as presented in 10.1007/s00023021010272 and study the system changing the topology of the network but maintaining fixed the total number of neurons. 
Anna Delmonte  SISSA
The Quantum Kuramoto model
Spontaneous synchronization is a collective phenomenon that can be observed in manybody interacting systems across many different fields.With the recent advancements in the field of quantum technologies, synchronization can now be observed in the quantum regime. Understanding this collective phenomenon in the quantum realm has become increasingly important, and theoretical models are still lacking.In the classical case, a prototypical example of synchronization is given by the Kuramoto Model, a model describing a system of interacting rotors. Its phase diagram supports both a dynamically disordered phase and a synchronized one. In this poster, I will propose a generalization of this model to the quantum realm, the Quantum Kuramoto Model. I will present how to build the quantum model and how it behaves, focusing on the differences between the classical and quantum regimes. 
Duilio De Santis  Dipartimento di Fisica e Chimica “Emilio Segrè”, Gruppo di Fisica Teorica Interdisciplinare, Università degli Studi di Palermo, Italia
Noiseinduced energy correlations and sineGordon breathers
In the acdriven sineGordon model, thermal noise is shown to be crucial for localizing energy into breather states. We indeed observe the emergence of remarkably stable breathers locked to the external drive, if the temperature is high enough. The energy spatial correlations, which display a nonmonotonicity versus the thermal noise strength, provide an intuitive statistical measure of the phenomenon. In further confirmation of the key role of noise as a control parameter, the breather generation probability also behaves nonmonotonically against the noise intensity. Then, we discuss the reliability of the approach for different breathing frequencies, as well as the influence of both topology and noise on the full counting statistics of the number, position, and amplitude of the excited breathers. With applications ranging from seismology and biology to highTc superconductivity and quantum Josephson electronics, mastering the physics of sineGordon breathers is a critical research task. Here, we exploit our findings to face a longunsolved challenge in nonlinear science, i.e., we propose a resistive switching experiment for detecting breathers in long Josephson junctions.Reference: D. De Santis, C. Guarcello, B. Spagnolo, A. Carollo, D. Valenti, Chaos, Solitons and Fractals 170 113382 (2023) 
Giovanni Di Fresco  Università degli Studi di Palermo
Quantum Fisher information: Unveiling measurement induced phase transitions in quantum systems
The interplay between a deterministic quantum evolution and a series of measurement processes can lead to a sudden change in the entanglement properties of a system, known as a measurementinduced phase transition (MIPT). Quantum Fisher information (QFI) measures the sensitivity of a quantum system to small changes in a parameter and is widely used to detect quantum phase transitions in different situations. It is natural to inquire whether QFI can also be employed to identify phase transitions driven by measurement processes. The distinctive characteristic of an MIPT is the abrupt alteration in the system's entanglement properties, typically assessed using entanglement entropy. However, with an appropriate metrological scheme, QFI not only detects entanglement but also provides more informative measurements than entanglement entropy. QFI detects multipartite entanglement and specifically highlights the presence of useful metrological entanglement. We show that QFI can distinguish among different phases in a MIPT for a nonHermitian onedimensional Ising chain and show the presence of a divergence of QFI at the critical point. 
Angelo Di Garbo  CNR Istituto di Biofisica, Pisa e Dipartimento di Fisica dell'Universita di Pisa
Complex dynamical regimes of relaxation oscillators describing UJT circuits
Diego Febbe (1), Riccardo Mannella (1), Riccardo Meucci (2), Angelo Di Garbo (3,1)(1) Dipartimento di Fisica dell’Università di Pisa, Pisa (Italia)(2) CNR – Istituto Nazionale di Ottica, Firenze (Italia)(3) CNR – Istituto di Biofisica, Pisa (Italia)This study presents a new mathematical model for a relaxation oscillator implemented using a unipolar junction transistor (UJT). The model is represented by a system of differential equations capable of reproducing the main features of experimental data. Then, the model was studied theoretically within the framework of nonlinear dynamical systems and the corresponding results were found to be in keeping with the numerical ones. In addition, the simulation show that when this dynamical system is subject to periodic modulation or to coupling, with an identical oscillators, chaotic dynamical regimes occur, in agreement with the experimental results. 
Alessandro Fiasconaro  Universidad de Zaragoza
Endpulled polymer translocation
Polymer translocation has long been a topic of interest in the field of biological physics given its relevance in both biological (protein and DNA/RNA translocation through nuclear and cell membranes) and technological processes (nanopore DNA sequencing, drug delivery).This contribution reports some recent results of the translocation of a semiflexible homopolymer through an extended pore driven by an endpulling force applied to the polymer head. Similarly to poredriven configurations, the endpulled setup presents regions of optimum in the mean translocation times as a function of the frequency of the driving –this latter applied either longitudinal to the pore or transversal to it– which are typical of the resonant activation effect. These minima are present for all the polymer rigidities studied, and reveal a linear relation between the optimum translocation time and the corresponding driving period independent of the parameter values.The endpulling driving, that mimics the optical or magnetic force application, has the potential to evidence specific features of either a nucleic or amino acid chains that the translocating polymer model aims to depict, making it a feasible candidate for a valid sequencing method.BibliographyA. Fiasconaro, J.J. Mazo, and F. Falo, Phys. Rev. E 82, 031803 (2010)J.A. Cohen, A. Chaudhuri, and R. Golestanian, Phys. Rev. Lett. 107, 238102 (2011)A. Fiasconaro, J.J. Mazo, and F. Falo, J. Stat. Mech. Theory Exp. P11002 (2011)T. Ikonen, J. Shin, W. Sung, and T. AlaNissila, J. Chem. Phys. 136, 205104 (2012)A. Fiasconaro, J.J. Mazo, and F. Falo, New Journal of Physics 14, 023004 (2012)J.R. Moffitt, Y.R. Chemla, K. Aathavan, …, and C. Bustamante, Nature 457, 446 (2009)J.R. Moffitt, Y.R. Chemla and C. Bustamante, Proc. Natl. Acad. Sci. USA 107, 15739 (2010)A. Fiasconaro, J.J. Mazo, and F. Falo, Phys. Rev. E 91, 022113 (2015)A. Fiasconaro, J.J. Mazo, and F. Falo, Sci. Rep. 7, 4188 (2017)A. Fiasconaro, and F. Falo, Phys. Rev. E 98, 062501 (2018)A. Fiasconaro, G. DíezSeñorans, and F. Falo, Polymer 259, 125305 (2022)A. SáinzAgost, A. Fiasconaro, and F. Falo, Submitted (2023) 
Paolo La Francesca  Università degli studi Roma Tre
Aqueous Perchlorate Solutions: a Numerical Study
The study of water in solutions plays a key role in the research regarding water anomalies both because aqueous solutions are naturally found in large quantities and because the experimental conditions under which many thermodynamic quantities are measured are more complicated to achieve for bulk water. Here we show the calculations of the phase diagrams of sodium perchlorate solutions in supercooled water derived through molecular dynamics numerical simulations. These solutions are relevant due to the recent experimental evidences of liquid water in perchlorate solutions beneath the Martian soil. By modelling water using the TIP4P/2005 potential, we obtain an agreement with the hypothesis of existence of a second order liquidliquid phase transition where the liquidliquid critical point shifts to slightly higher temperatures and lower pressures. By investigating the structure of the systems, we find that even at the highest concentrations considered, water retained its anomalous behaviour. 
Emanuele Locatelli  Department of Physics and Astronomy, University of Padova
Interplay between topology and confinement in active polymers
Active systems, due to the local breaking of equilibrium, allow for phenomena that their equilibrium counterparts cannot attain. This correspondence between microscopic local equilibrium breaking and the meso/macroscopic structure formation is a general feature that have been observed in diverse systems including bacteria and synthetic swimmers. A similar behaviour can be observed also in the case of polar active polymers, i.e. polymers made of active monomers whose activity is directed as the local tangent to the polymer backbone. For example, a coiltoglobulelike transition takes place for isolated active chains in three dimension, highlighted by a marked change of the scaling exponent of the gyration radius[1]. Driven by the relevance of confinement and topology on the structural and dynamical properties of passive systems, we investigate the interplay between these latter and activity for tangentially active polymers. We explore the dynamics of active polymers in corrugated channels, highlighting the differences with respect to the passive case[2]. In the bulk, isolated rings display two different regimes at high enough activity: short rings tend to become ”stiffer” and to assume a disklike conformation, whereas long rings collapse, forming tight structures that show the hallmarks of dynamical arrest[3]. Finally, when placed under confinement, suspensions of short active rings assemble in ordered phases [4].References[1] V. Bianco, E. Locatelli, and P. Malgaretti, Phys. Rev. Lett. 121, 217802 (2018).[2] J. Marti Roca, E. Locatelli, V. Bianco, P.Malgaretti and C. Valeriani, in preparation[3] E. Locatelli, V. Bianco, and P. Malgaretti, Phys. Rev. Lett. 126, 097801 (2021).[4] J.P. Miranda, E. Locatelli and C. Valeriani, in preparation 
Gianluca Manzan  Università di Bologna
Efficiency limits of Restricted Boltzmann Machines in teacherstudent frameworks
Unsupervised Machine learning with Boltzmann machines is the inverse problem of finding a suitable Gibbs measure to approximate an unknown probability distribution from a training set consisting of a large amount of samples. The minimum size of the training set necessary for a good estimation depends on both the properties of the data and of the machine. We investigate this problem in a controlled environment where a Teacher Restricted Boltzmann machine (TRBM) is used to generate the dataset and another student machine (SRBM) is trained with it. We consider different classes of unit priors and weight regularizers and we analyze both the informed and mismatched cases, viewed as the amount of information the student receives about the teacher model. We describe the results in terms of phase transitions in the posterior distribution, interpreted as a statistical mechanics system.In the analysis we give special attention to the Hopfield model case where it is possible to observe the differences between memorization and learning regimes. In particular, when data become large and confused the learning methodology overcomes memorization.References:Hopfield model with planted patterns: a teacherstudent selfsupervised learning model Alemanno, F., Camanzi, L., Manzan, G., Tandari, D. (2023). arXiv:2304.13710.Phase diagram of restricted Boltzmann machines and generalized Hopfield networks with arbitrary priors Barra, A., Genovese, G., Sollich, P., & Tantari, D. (2018). Physical Review E, 97(2), 022310.Phase transitions in restricted Boltzmann machines with generic prios Barra, A., Genovese, G., Sollich, P., & Tantari, D. (2017). Physical Review E, 96(4), 042156.Restricted Boltzmann machine: Recent advances and meanfield theory Decelle, A., & Furtlehner, C. (2021). Chinese Physics B, 30(4), 040202.On the equivalence of Hopfield networks and Boltzmann Machines Barra, A., Bernacchia, A., Santucci, E., & Contucci, P. (2012). Neural Networks, 34, 19. Statistical Mechanics of Neural NetworksHuang, H. (2022). Springer. Theory of neural information processing systems Coolen, A.C., Kühn, R. and Sollich, P. (2005). OUP OxfordStatistical physics of spin glasses and information processing: an introduction (No. 111)Nishimori, H., 2001 Clarendon Press. 
Davide Marcato  SISSA  Trieste
Lattice model of semiflexible and selfinteracting polymer solutions: A meanfield approach
We study a lattice model in d dimensions for a system of multiple self (and mutally) avoiding chains. A bending rigidity and a nonconsecutive nearestneighbour monomermonomer interaction are accounted for as well. First, we present an exact fieldtheoretical representation of the gran canonical partition function (based on the analogy between SAWs on a lattice and the O(n > 0) model of a magnet) in the ensemble in which nor the total number of bonds nor the total number of chains is fixed. We then give a meanfield estimate of such partition function by means of a uniform saddlepoint approximation, and hence derive expressions for physical observables. We find a discontinuity in the total monomer density as a function of the bond and chain fugacity, revealing the presence of a gas  liquid transition. All the results are compared with Monte Carlo computer simulations, showing a remarkable agreement. Lastly, we provide an expression for the free energy variation upon mixing, and discuss how our findings relate to the classical FloryHuggins theory for polymer solutions. 
Andrea Maroncelli  Università di Firenze
The arctic curves of the fourvertex model
We consider the fourvertex model, which is a special case of the sixvertex model in which two vertices are set to zero. Under specific choices of fixed boundary conditions, this model exhibits spatial phase separation, between frozen and disordered regions, sharply separated by a smooth curve, known as arctic curve. The most interesting aspect of the fourvertex model is that, even though it is interacting, it is still exactly solvable in a relatively simple way. Here we use the Tangent Method, which is an exact, although heuristic method, to compute the arctic curve. 
Giovanni Mattiotti  Università di Trento
Dynamical characterization of a CCMV virion and its constituents
An increasing amount of structural information about the protein capsid of viruses has been collected and is now available in the Protein Data Bank; yet, the intrinsically disordered nature of viral ssRNA structures poses a challenge for experimentalists, this being critical on account of the impact that the RNA structure has on its function. In this concern, molecular dynamics simulations might be powerful tools to achieve (putative) structural and dynamical insights on the behaviour of systems that are poorly characterized.In this poster, I will discuss the main results of our ongoing project on the development of new methodologies to characterize the unrestrained dynamics of a viral RNA fragment as well as under spatial constraints mimicking the protein capsid around it. I will then show the performance of simulating a trimer (the basic building block of the capsid) with an implicit solvent model with an inhouse developed multiresolution model. I will also describe a simple and general protocol to generate an initial configuration of the whole virion particle to perform allatom MD simulations, starting from a PDB structure of the capsid and the sequence of the RNA fragment. This approach will provide detailed information about the structure and dynamics of the viral RNA, involving a description of the interactions between the nucleotides and the tails of the capsid, which is hardly explorable via experimental techniques. Finally, I will show some preliminary results obtained by simulating the virion and the capsid at atomistic resolution. 
Enea Mauri  Fondazione Bruno Kessler
EPIQUS: portable quantum computing with photons
Quantum computing is attracting a lot of attention for its potential to greatly speedup some computations and to perform efficient simulations of the dynamics of quantum systems. Among all the possible platforms, integrated linear optics allows for the realization of a compact device that operates at room temperature, exploiting boson statistics to perform quantum simulations and computations. EPIQUS (ElectronicPhotonic Integrated QUantum Simulator) aims to build a reconfigurable, fullyintegrated linear optical quantum hardware with singlephoton sources and detectors.
In this poster we describe the inner working of such a device, highlighting its capabilities as well as some of its shortcomings.

Margherita Mele  Physics Department, University of Trento, via Sommarive, 14 I38123 Trento, Italy
Exploring the weight space of a perceptron via enhanced sampling techniques
The steadily growing computing power has made vast amounts of highthroughput data available, opening new windows into complex systems such as cells, the brain, and human societies. However, while the staggering success of Artificial Intelligence and Machine Learning revealed the potential of neural networks, it also raised crucial theoretical questions about them, first and foremost: how does learning take place? In artificial neural networks, learning translates in tuning a large number of connection weights to minimise a loss function. The assumption of Gaussian i.i.d. inputs has been fundamental to the theoretical and computational study of highdimensional learning; answering the question of whether and how far this hypothesis is restrictive has now become imperative. In our work we have taken advantage of enhanced sampling methods [1], developed in soft matter physics, to exhaustively explore the loss profile of networks with discrete weights, where the optimization landscape is severely rugged even for simple architectures. These tools have proven to be very powerful as they can be directly applied to real datasets, thus allowing us to explore the impact of dimensionality and structure of the data. In particular, we have investigated 4 widely used benchmark datasets: MNIST, FashionMNIST, CIFAR10 and MNIST1D. For each of them we analysed the role of the structure as well as the impact of the inputoutput correlation. Additionally, this approach enables us to prove whether or not the universality of linear classification with random labels [2] may be extended also in case of nonconvex loss and for energetic states higher than the ground state. [1] Menichetti, R., Giulini, M., & Potestio, R. (2021). The European Physical Journal B, 94, 126.[2] Gerace, F., Krzakala, F., Loureiro, B., Stephan, L., & Zdeborová, L. (2022). arXiv preprint arXiv:2205.13303. 
Roberto Menichetti  Department of Physics, University of Trento
Investigating biological systems via maximally informative reduced representations
The relentless development of novel computer architectures and algorithms is steadily pushing forward the limits of the investigation of biological systems via "in silico" simulations. This process goes on par with an explosion in the amount of generated data, calling for the design of innovative and automated techniques able to rationalise the simulation outcomes and extract the biologically relevant insight out of them.In the analysis of such complex systems, the noise/signal discrimination quite often naturally passes through a coarsegrained filtering procedure in which, starting from the most detailed description available, a projection is performed that forces the system to be observed only in terms of a subset of its original degrees of freedom [1]e.g., a fraction of atoms in a protein or of neurons in a neural network. While necessary for interpreting otherwise hardlymanageable highdimensional datasets, this workflow results in a loss of statistical information on the system, loss that critically depends on the filter one selects to carry out the projection [2,3].In this work we discuss a recently introduced strategy aimed at identifying maximally informative simplified representations of a system that, despite a reduction in the observational level of detail, are capable of retaining the largest amount of information on the statistical properties of the highresolution reference [3,4]. We apply this protocol to two very different classes of systems within the biological realm, namely proteins and memoryretrieving neural networks; in both cases, the resulting maximally informative representations are shown to single out biologically relevant regions of the system, either in the form of functional chemical fragments in the analysed protein, or in the form of strongly coupled neurons inside the synaptic matrix.Overall, these results demonstrate that this scheme can be successfully employed to extract crucial physicochemical information out of large simulation datasets in an unsupervised manner, further shedding light on the relation between coarsegraining and loss of statistical information.[1] M. Giulini, R.M. et al., Front. Mol. Biosci. 8 (2021).[2] J. F. Rudzinski and W. G. Noid, J. Chem. Phys. 135, 214101 (2011).[3] M. Giulini, R.M. et al., J. Chem. Theory Comput. 16, 6795 (2020).[4] R. Holtzman et al., Phys. Rev. E 106, 044101 (2022). 
Manuel Micheloni  University of Trento
Kinetics of radiationinduced DNA doublestrand breaks through coarsegrained simulations
Double strand breaks (DSBs), i.e. the covalent cut of the DNA backbone over both strands, are a detrimental outcome of cell irradiation, bearing chromosomal aberrations and leading to cell apoptosis. In the early stages of the evolution of a DSB, the disruption of the residual interactions between the DNA moieties drives the fracture of the helical layout; in spite of its biological significance, the details of this process are still largely uncertain. Here, we address the mechanical rupture of DNA by DSBs via molecular dynamics simulations: the setup involves a 3855bp DNA filament and diverse DSB motifs, i.e. within a range of distances between strand breaks (or DSB distance). By employing a coarsegrained model of DNA, we access the molecular details and characteristic timescales of the rupturing process. A sequencenonspecific, linear correlation is observed between the DSB distance and the internal energy contribution to the disruption of the residual (WatsonCrick and stacking) contacts between DNA moieties, which is seemingly driven by an abrupt, cooperative process. Moreover, we infer an exponential dependence of the characteristic rupture times on the DSB distances, which we associate to an Arrhenius law of thermallyactivated processes. This work lays the foundations of a detailed, mechanistic assessment of DSBs in silico, as a benchmark to both numerical simulations and data from single molecule experiments. 
Matteo Milazzo  Università di Catania
On the Heterogeneity of Households’ portfolios in the Nordic Stock Market
Financial markets are complex systems where many market participants act with different aims and needs. The overall behavior of the market depends by the interrelations of trading choices of market participants. We focus our attention on the category of households, confronting the trading choices of this wide category of market participants with other trading categories such as financial and nonfinancial companies. The data analyzed are obtained from the Euroclear clearing house that is the clearing house of the Nordic Stock Exchange. Data [1,2] cover the time span from January 1996 to December 2016 and cover the entire population of distinct Finnish legal entities. In our analysis, we compute semestral portfolios for each legal entity owning financial assets traded in the Nordic Stock Exchange. For the sake of simplicity, we chose to focus on the most liquid stocks, i.e., the ones included in the OMXH25 market index. We investigate heterogeneity of investors’ portfolios by quantifying the degree of concentration of each portfolio with the Herfindahl Index of it. The Herfindahl index is a measure of concentration, introduced in economics and widely used in many research areas.We compute the Herfindahl index [3] of portfolios of all Finnish households investing in the Nordic Stock Exchange on a semiannual basis for the entire time span of data. For the category of households, the mean value of the index decreases slowly but steadily over the years showing an increase of the diversification over the number of stocks selected in the portfolio over time. We compare the dynamics of the mean Herfindahl index with the dynamics of the overall portfolio owned by the category of households. Our analysis shows that the households’ market portfolio shows a different degree of heterogeneity than the one observed for the mean behavior of individual households. In fact, the aggregated portfolios for the households, which represent the largest category of investors, has a trend, over the years, that is similar to the aggregated portfolio of financial companies. This empirical observation suggests that households as an investors’ category distribute their resources in a way that is not too different form the distribution done by professionals. The different time profile of the Herfindahl index of portfolio of all the households and the mean Herfindahl index estimated portfolios of all of them, suggest that heterogeneity in wealth and asset selection is highly present in the households acting in this market.[1] Tumminello, M., Lillo, F., Piilo, J. and Mantegna, R.N., 2012. Identification of clusters of investors from their real trading activity in a financial market. New Journal of Physics, 14(1), p.013041.[2] Musciotto, F., Marotta, L., Piilo, J. and Mantegna, R.N., 2018. Longterm ecology of investors in a financial market. Palgrave Communications, 4(1), pp.11.[3] Hall, M.; Tideman, N.1967 Measures of concentration. J. Am. Stat. Assoc. 62, 162–168.Joint work with Federico Musciotto, Jyrki Piilo, Rosario N. Mantegna 
Luca Guido Molinari  Dipartimento di Fisica Aldo Pontremoli, Milano
Graphene nanocones and Pascal matrices
I conjecture an identity among the determinant of the adjacency matrix of a graphene nanocone with Bloch b.c. and the characteristic polynomial p(z) of a Pascal matrix. The latter is analytically known only for z equal to some roots of unity, related to counting problems of partitions, or lozenge tilings of an hexagon, or dense loops on a cylinder. 
Jacopo Niedda  Sapienza, University of Rome
Glass and pseudolocalization transitions in the glassy random laser
Optical waves in active disordered media display the typical phenomenology of complex systems. Several spectral shots taken from the same piece of material in the lasing regime display strong fluctuations in the position of the intensity peaks, suggesting that there is no specific mode which is preferred in the amplification, but depending on the initial state, with the disorder kept fixed, the modes gaining the highest intensity change every time. In order to explain this behaviour, a spinglass model has been developed, where the light modes are described as nonlinearly interacting phasors on the socalled modelocked diluted graph [1]. The specific modecoupling selection rule, which naturally emerges in the study of lasing modes dynamics, impairs the analytical solution of the model out of the narrow bandwidth limit, where the interaction network is fully connected. In this talk we present recent results from numerical simulations of the modelocked glassy random laser. A phenomenology compatible with a glass transition is revealed from the divergence of the specific heat and the nontrivial structure of the Parisi overlap distribution function. By means of a refined finitesize scaling analysis of the critical region, the transition is assessed to be compatible with a meanfield universality class [2]. A pseudolocalization transition to a phase where the intensity of light is neither properly localized on a single mode nor equiparted among all the modes is revealed from the measure of the inverse participation ratio and of the spectral entropy [3]. The two transitions occur at the same temperature as different manifestations of the same underlying phenomenon, the breaking of ergodicity.[1] F. Antenucci, C. Conti, A. Crisanti and L. Leuzzi, Phys. Rev. Lett. 114, 043901 (2015).[2] J. Niedda, G. Gradenigo, L. Leuzzi and G. Parisi, arXiv:2210.04362, (2022).[3] J. Niedda, L. Leuzzi and G. Gradenigo, arXiv:2212.05106 (2022). 
Stefano Pierini  Università di Napoli Parthenope
The deterministic excitation paradigm and the glacialinterglacial transitions
A deterministic excitation (DE) paradigm is formulated [1], according to which the abrupt glacialinterglacial transitions that occurred after the MidPleistocene Transition correspond to the excitation, by the orbital forcing, of nonlinear relaxation oscillations internal to the climate system in the absence of any stochastic parameterization. Specific threshold crossing rules parameterizing the activation of internal climate feedbacks leading to relaxation oscillation excitations, are derived according to the DE assumption. Such rules are then applied to the fluctuations of the glacial state simulated by an energy balance model subjected to realistic orbital forcing. The timing of the glacial terminations thus obtained in a reference simulation is found to be in good agreement with proxy records; besides, a sensitivity analysis insures the robustness of the timing. The role of noise in the glacialinterglacial transitions, and the problems arising in the implementation of theories in which noise is crucial (such as stochastic resonance) are finally discussed. In conclusion, the DE paradigm provides the simplest possible dynamical systems characterization of the link between orbital forcing and glacial terminations implied by the Milankovitch hypothesis.[1] Pierini, S., 2023: The deterministic excitation paradigm and the late Pleistocene glacial terminations. Chaos, 33, 033108, https://doi.org/10.1063/5.0127715. 
Ernesto Pini  Università di Firenze
Observation of Non Selfsimilar light transport
In this work, I report on experimental timeresolved measurements of light transport through weakly scattering membranes based on a subps optical gating imaging technique. We characterized simple scattering slabs comprising different volume densities of TiO2 nanoparticles, finding spatial intensity distributions which exhibit different profiles at different times, and which spread with an enhanced transverse propagation rate with respect to the nominal transport mean free path. We propose an analysis of the resulting spatiotemporal profiles based on the concept of “selfsimilarity”, that relies on the study of all spatial moments of displacements of the transient intensity profiles. Our results show the emergence of an anomalous transient regime which persists after several scattering events, and arises in spite of the homogeneous and isotropic structure of the investigated samples. Experimental data are in excellent agreement with numerical Monte Carlo simulations, showing that the concept of selfsimilarity is a particularly useful tool to study general transport phenomena and their deviations from standard diffusive propagation. 
Santi Prestipino  Università degli Studi di Messina
Supersolid phases of bosonic particles in a bubble trap
Confinement can have a considerable effect on the behavior of particle systems, and is therefore an effective way to discover new phenomena. A notable example is a system of identical bosons at low temperature under an external field mimicking an isotropic bubble trap, which constrains the particles to a portion of space close to a spherical surface. Using Path Integral Monte Carlo simulations, we examine the spatial structure and superfluid fraction in two emblematic cases. First, we look at softcore bosons, finding the existence of supersolid cluster arrangements with polyhedral symmetry; we show how different numbers of clusters are stabilized depending on the trap radius and the particle mass, and we characterize the temperature behavior of the cluster phases. A detailed comparison with the behavior of classical softcore particles is provided too. Then, we examine the case, of more immediate experimental interest, of a dipolar condensate on the sphere, demonstrating how a quasionedimensional supersolid of clusters is formed on a great circle for realistic values of density and interaction parameters. We argue that the predicted phases can be revealed in magnetic traps with sphericalshell geometry. Our results pave the way for future simulation studies of correlated quantum systems in curved geometries. 
Leonardo Salicari  University of Padova, INFN sezione di Padova
Folding kinetics of an entangled protein
The possibility of the protein backbone adopting lassolike entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled singledomain proteins, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyse simulations of a coarsegrained, structurebased model for a small singledomain protein. Despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a shortlived, entangled, nearunfolded state and a longlived, nonentangled, nearnative state. The entangled state promotes fast refolding, while the nonentangled state acts as a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop forms without being threaded by the Nterminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, the earlier the native contacts form, the more their formation time may fluctuate. Trapping does not occur because the native contacts at the closure of the lassolike loop form after those involved in the Nterminal thread, confirming previous predictions. Remarkably, a longlived, nearnative intermediate, with nonnative entanglement properties, recalls what was observed in cotranslational folding. 
Yonathan Sarmiento  SISSAICTP
Perceptual decision making of nonequilibrium fluctuations
In studying perceptual decision making, the common neuroscientific approach is to measurebehavior, its accuracy, and speed, and then analyze it with mathematical models to makeinferences on the underlying mechanism. In this work, we turn this approach around and froma model with the physical properties of a stimulus moving according to a nonequilibriumstationary stochastic process [1], we predict the decision time of human participants. In abehavioral experiment, we asked 21 young healthy participants to judge the motion directionof a visual stimulus moving with a given drift velocity and diffusion coefficient. The rate ofstochastic entropy production that emerged from the trajectory of the stimulus allowed us tomeasure the noise in the system. Results revealed an inverse proportionality relation betweenthe participants’ mean decision time and the rate of entropy production of the underlyingphysical process, establishing an analytical approach to predict the amount of time requiredto extract the signal under uncertainty. In addition to that, having a strong link between thedynamics of the stimulus trajectory and the decision outcomes led us to investigate the sourceof the variability in decision parameters and revealed a pattern of trialbytrial evidenceintegration. Overall, our study shows that providing a detailed model of the physical propertiesof the stimuli to judge allows a better characterization of the variables influencing perceptualdecisions and refines our understanding of the temporal dynamics of efficient evidenceintegration.[1] E. Roldan, I. Neri, M. Dorpinghaus, H. Meyr, F. Julicher, Decision making in the arrow oftime. Physical review letters 115(25), 250, 602 (2015). 
Fabio Sartori  KIT  Karlsruhe Instutute fur technology
The Impact of Behavior Polarization and Homophily on Epidemics
In the last 30 years, several hundred articles studied the interplay between the feedback loop between the evolution of an outbreak and the change in behavior of the involved individuals.Each model makes unique predictions about the distribution of selfprotecting behavior and its clustering. For example, in imitation games, such as [FU2011], an individual will mimic the behavior of a neighbor with a higher payoff, leading to a higher level of homophily (clustering) within the network; conversely, with a gametheory approach, as in [XIA2013], a higher fraction of selfprotecting neighbors decrease the perception of the risk and the selfprotecting probability.This work studies the impact on several disease models and networks of behavior polarization and homophily.When the behavior of an agent represents the individual level of attention, and it rescales the infectivity $\beta$, we show that both homophily and polarization significantly impact an outbreak's evolution even if the average infectivity is fixed; This is an important insight for building compartmental models: knowing the average value of the infectivity of each agent is not enough to predict the evolution of an outbreak.[FU2011] Fu, Feng, et al. "Imitation dynamics of vaccination behaviour on social networks." Proceedings of the Royal Society B: Biological Sciences 278.1702 (2011): 4249.[XIA2013] Xia, Shang, and Jiming Liu. "A computational approach to characterizing the impact of social influence on individuals' vaccination decision making." PloS one 8.4 (2013): e60373. 
Francesco Slongo  SISSA, Trieste
Sampling ring melts with quantum computer
TBA 
Andrea Solfanelli  SISSA
Tricritical point in the quantum Hamiltonian meanfield model
Engineering longrange interactions in experimental platforms has been achieved with great success in a large variety of quantum systems in recent years. Inspired by this progress, we propose a generalization of the classical Hamiltonian meanfield model to fermionic particles. We study the phase diagram and thermodynamic properties of the model in the canonical ensemble for ferromagnetic interactions as a function of temperature and hopping. At zero temperature, small charge fluctuations drive the manybody system through a firstorder quantum phase transition from an ordered to a disordered phase. At higher temperatures, the fluctuationinduced phase transition remains first order initially and switches to secondorder only at a tricritical point. Our results offer an intriguing example of tricriticality in a quantum system with longrange couplings, which bears direct experimental relevance. The analysis is performed by exact diagonalization and meanfield theory. 
Vittoria Sposini  University of Vienna
Characterising the slow dynamics of the Gaussian Core Model
Within the realm of soft colloids a prominent role is played by the Gaussian Core Model (GCM) introduced by Stillinger in the 70’s [1]. The GCM describes point particles interacting by means of a Gaussianshaped potential and is one of the simplest models for the description of systems such as polymer or dendrimer solutions [2, 3].Whereas at low temperatures and densities the GCM is believed to be described by an effective hardsphere mapping, at high densities a meanfield description sets in, giving rise to reentrant melting [4] and a glass state compatible with a geometric transition [5]. The broad intermediate glassy regime remains unexplored [6]. In this talk I will present results from molecular dynamics simulations exploring the slow dynamics of the GCM in this regime. In particular, I will discuss the transition from the low density hardspherelike glassy dynamics to the high density one, featuring novel interesting characteristics that we attribute to the interplay between temperature and soft decay tail of the GCM.[1] F. H. Stillinger, J. Chem. Phys. 65, 3968 (1976).[2] A. A. Louis et al., Phys. Rev. Lett. 85, 2522 (2000).[3] I. O. Goetze et al., J. Chem. Phys. 120, 7761 (2004).[4] A. Lang et al., J. Phys.: Condens. Matter 12, 5087 (2000).[5] D. Coslovich et al., Phys. Rev. E 93, 042602 (2016).[6] JM. Bomont et al., Phys. Rev. E 105, 024607 (2022). 
Thomas Tarenzi  University of Trento
CANVAS: A Fast, Accurate, and SystemSpecific Variable Resolution Approach for Simulating Biomolecules
The field of multiscale modeling and simulation has enjoyed significant success in soft matter research within the past decade also thanks to the boost impressed by the necessity to overcome the expensive cost of a single, highly detailed resolution. Several methodologies have been developed in the past few years, where different system components are simultaneously modelled at different levels of resolution [1]. In the case of biomolecules, functionally relevant parts of the system can be modelled at a high a level of detail, while the remainder of the system can be represented using less expensive models. Here, we propose a novel multiresolution scheme dubbed coarsegrained anisotropic network model for variable resolution simulations, or CANVAS, which allows one to employ and smoothly couple virtually any desired degree of coarsegraining within the same model [2]. The novelty of this method lies in the possibility of setting the level of resolution of the coarsegrained subdomains in a quasicontinuous range; furthermore, the interaction network within and between resolution domains is straightforwardly parametrized on the basis of the properties of the specific system under examination. The model is validated by comparing results from allatom and multiscale simulations of two biomolecules, namely the enzyme adenylate kinase and the IgG4 antibody pembrolizumab.[1] Giulini, M. et al., 2021. Frontiers in Molecular Biosciences, 8, p.676976.[2] Fiorentini, R. et al., 2023. Journal of Chemical Information and Modeling, 63(4), pp.12601275. 
Davide Valenti  Università di Palermo
Random fluctuations of solar irradiance: effects on the dynamics of a marine ecosystem
The analysis of experimental data of the solar irradiance, collected on the sea surface, highlights the intrinsic stochasticity of such an environmental variable. Given this result, the effects of randomly fluctuating irradiance on the population dynamics of a marine ecosystem are studied on the basis of the stochastic 0dimensional biogeochemical flux model (BFM). The noisy fluctuations of the irradiance are formally described by a multiplicative OrnsteinUhlenbeck process, i.e., a selfcorrelated Gaussian noise. Nonmonotonic behaviours of the variance of the marine populations’ biomass are found with respect to the intensity and the autocorrelation time of the noise source, manifesting a noiseinduced transition of the ecosystem to an outofequilibrium steady state. Moreover, noiseinduced effects in the organic carbon cycling processes, underlying the food web dynamics, are observed. These findings clearly show the profound impact the stochastic behaviour of environmental variables can have on both biological and chemical components of a marine trophic network. 
Francesca Vercellone  Università degli Studi di Napoli Federico II
Polymer physics and Machine Learning infer the code underlying chromosome folding
Rapid innovations in Molecular Biology have shed light on the 3D arrangement of DNA within the cell nucleus, revealing its complex, nonrandom character, and its connection to gene regulation. In any case, the mechanisms that regulate DNADNA contacts are still poorly understood to date. Polymer physics and Machine learning approaches are proving to be excellent tools for investigating these phenomena. In this work, we infer from only HiC data the celltypespecific arrangement of DNA binding sites able to recapitulate, through polymer physics, contact patterns genome wide. The binding site types fall in classes that show an overlapping, combinatorial organization along chromosomes necessary to accurately explain contact specificity. The chromatin signatures of the binding site types return a code linking chromatin states to 3D conformation. The code is validated by de novo predictions of HiC maps in independent chromosomes. Furthermore, we investigate the range of applicability of this code among cell types by making predictions on HiC data from another cell line, different from the one used to obtain the code itself. Overall, our results shed light on how 3D information is encrypted in 1D chromatin via the specific combinatorial arrangement of binding sites.Ref:Esposito A. et al. Polymer physics reveals a combinatorial code linking 3D chromatin architecture to 1D chromatin states. Cell Reports, 2022.Conte M. et al. Unveiling the Machinery behind Chromosome Folding by Polymer Physics Modeling. International Journal of Molecular Sciences, 2023. 
Michele Vodret  CentraleSupélec
Irreversible Dynamics and Maximum Entropy Production in Human Biased Learning
The assumption of rational traders has been the subject of a harsh debate in theoretical economics for the past 40 years. Recent experimental evidence gathered by cognitive neuroscientists suggests that the way we learn in simple tasks is in stark contrast with the rationality assumption: the way we learn is biased. Confirmation bias, for example, is the tendency to incorporate the information in line with our priors and disregard the information in contrast with them.These findings beg for an explanation. In particular, if evolution selected such biases, they should be beneficial in some circumstances: for example, in tasks with two asymmetric bandits, there are 'optimal biases' which allow individuals to increase the average earned reward. The reason for these additional gains is that biased beliefs are magnifying, allowing one to distinguish more clearly between two similar options.Interestingly, in these contexts, the optimal bias corresponds to a learning dynamics that breaks detailed balance, leading, therefore, to irreversible dynamics, even in the stationary state. We argue, by means of analytical calculations and numerical simulations, that the optimal bias corresponds to dynamics that maximise the entropy production in the stationary state. In particular, in this context, the stationary state with maximum entropy production allows agents to safely explore the environment without being stuck in a suboptimal belief. 