Non-equilibrium dynamics in complex networks via asymmetric Glauber models

Abstract This paper explores the Glauber dynamics of spin systems with asymmetric coupling, a scenario that inherently violates detailed balance, leading to non-equilibrium steady states. By focusing on weighted and heterogeneous networks, we extend the applicability of Glauber models to capture complex real-world interactions, such as those seen in multilayer and hierarchical systems. Under specific assumptions on the coupling matrix, we demonstrate the tractability of these dynamics in the limit as the number of spins approaches infinity. Our results highlight the influence of network topology on dynamic behavior and provide a framework for analyzing stochastic processes in diverse applications, from statistical mechanics to data-driven modeling in applied sciences. The approach also uncovers potential for leveraging non-equilibrium dynamics in machine learning and network analysis.