Bayesian Inference and Non-Equilibrium Statistical Physics of Complex Networks for Brain Dynamics

The study of complex systems out of equilibrium represents one of the most challenging frontiers of Physics. Unlike equilibrium systems, where statistical mechanics provides a clear framework based on the Hamiltonian and Boltzmann-Gibbs distributions, non-equilibrium systems lack a general potential function and their dynamics are fundamentally constrained by the breakdown of detailed balance. Nevertheless, recent advancements in stochastic thermodynamics have introduced powerful theoretical tools, most notably the Onsager-Machlup action functional and Graham’s quasi-potential, which enable a quantitative characterization of non-equilibrium steady states and transition paths. The primary objective of this Thesis is to develop a Bayesian inference framework grounded in the statistical physics of complex networks, based on the Onsager-Machlup action functional and the Graham’s quasi-potential, to reconstruct network topology from non-equilibrium dynamics. To validate this approach, out-of-equilibrium dynamics are generated using the stochastic Kuramoto model across various synthetic network topologies; computational simulations are performed under varying noise levels and coupling strengths, in order to rigorously test the inference feasibility, robustness, and accuracy of the framework. This Thesis aims to provide a novel methodological contribution to network theory and to neuroscience, considering out-of-equilibrium brain dynamics as the primary target to develop quantitative tools for investigating how complex brain networks maintain functionality and metastability.