Andrea Filippo Beretta — University of Padua #
Information-thermodynamic principles unveil the response of complex networks to perturbations #
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.