Beyond Equilibrium: Non-Equilibrium Foundations Should Underpin Generative Processes in Complex Dynamical Systems

This position paper argues that next-generation non-equilibrium-inspired generative models will provide the essential foundation for better modeling real-world complex dynamical systems. While many classical generative algorithms draw inspiration from equilibrium physics, they are fundamentally limited in representing systems with transient, irreversible, or far-from-equilibrium behavior. We show that non-equilibrium frameworks naturally capture non-equilibrium processes and evolving distributions. Through empirical experiments on a dynamic Printz potential system, we demonstrate that non-equilibrium generative models better track temporal evolution and adapt to non-stationary landscapes. We further highlight future directions such as integrating non-equilibrium principles with generative AI to simulate rare events, inferring underlying mechanisms, and representing multi-scale dynamics across scientific domains. Our position is that embracing non-equilibrium physics is not merely beneficial--but necessary--for generative AI to serve as a scientific modeling tool, offering new capabilities for simulating, understanding, and controlling complex systems.