11:55-12:45 Friday, 23 May 2025 Auditorium, Rectorate
Abstract
The application of Statistical Mechanics to the socio-technical complex systems is one of the goal of Complex Systems Physics. The theory of complex networks has been developed to study the interaction structures among the elementary components and to define university classes. But when one considers the relation among the microscopic dynamics, the structure of the interaction networks and the evolution of the macroscopic properties of a complex system, few theoretical results have been achieved. The random walks on graphs have been considered to develop a non-equilibrium statistical mechanics in the relaxation process or in the case of non-equilibrium stationary states (NESS). The relation between the spectral properties of the Laplacian matrices associated to random walks and the statistical mechanics approach is still not completely understood. We show as the concept of Von Neumann Entropy defined for a quantum system associated to a random walk allows to interpret the relaxation process of a random walk as an evolution on maximum entropy states if the detailed balance condition is satisfied and we discuss the possible extension to generic Markov systems. We consider the application of the Minimum Entropy Production Principle to cope with the problem of defining maximum entropy Markov models for complex systems, when one knows the geometrical structure of the transition network among the states. We show the possible applications of this approach to define data driven Markov models for urban mobility when partial information on the traffic flows is available. Our goal is to infer a null dynamical model that allows to study the relaxation process, the fluctuation statistics at the stationary state and the robustness of the stationary state to external or parametric perturbations using the spectral properties of the transition rate matrix.