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

Jiazhen Liu, Ruikun Li, Huandong Wang, Zihan Yu, Chang Liu, Jingtao Ding, Yong Li

TL;DR

This paper argues that generative modeling for complex dynamical systems must be grounded in non-equilibrium statistical mechanics to accurately capture time-asymmetric, dissipative processes. Through a theoretically framed comparison and a Printz-potential experiment, it shows non-equilibrium diffusion-based methods better track evolving distributions than equilibrium Boltzmann sampling. It surveys a spectrum of non-equilibrium approaches—diffusion models, Schrödinger bridges, Poisson flows, flow-based and non-equilibrium EBMs—and discusses how physical priors like entropy production can guide model design. The work highlights a path toward AI for science capable of simulating, inferring, and controlling multi-scale, non-stationary dynamics across physical, biological, and engineered domains.

Abstract

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.

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

TL;DR

This paper argues that generative modeling for complex dynamical systems must be grounded in non-equilibrium statistical mechanics to accurately capture time-asymmetric, dissipative processes. Through a theoretically framed comparison and a Printz-potential experiment, it shows non-equilibrium diffusion-based methods better track evolving distributions than equilibrium Boltzmann sampling. It surveys a spectrum of non-equilibrium approaches—diffusion models, Schrödinger bridges, Poisson flows, flow-based and non-equilibrium EBMs—and discusses how physical priors like entropy production can guide model design. The work highlights a path toward AI for science capable of simulating, inferring, and controlling multi-scale, non-stationary dynamics across physical, biological, and engineered domains.

Abstract

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.

Paper Structure

This paper contains 15 sections, 32 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Revisiting Generative Models Through Statistical Mechanics
  3. Energy-based generative models inspired by equilibrium statistical mechanics
  4. Generative models inspired by non-equilibrium statistical mechanics
  5. The connection of non-physics-inspired generative models to statistical physics
  6. Non-Equilibrium Generative Modeling Better Captures Dynamics in Evolving Systems
  7. Outlook or future directions
  8. Potential future application to physical science and complex systems
  9. Non-equilibrium physics for more advanced generative models
  10. Alternative Views
  11. Representative cases of generative models driven by non-equilibrium stochastic dynamics
  12. Generating samples by the Fokker-Planck equation.
  13. Asymptotical independency of the initial state for the Brownian motion
  14. Experiment on a time-varying potential system
  15. Generative models in various physics systems

Figures (3)

  • Figure 1: Equilibrium vs. non-equilibrium generation on a time-varying potential system. (a) Potential & dynamics equations. (b) Generation error comparison. (c) True energy landscape (left), non-equilibrium gradient field (mid), equilibrium energy field (right). (d) Generated distribution by non-equilibrium method.
  • Figure 2: Outlook or future directions of both non-equilibrium physics and generative AI.
  • Figure 3: Physical systems invoke non-equilibrium thermodynamics and the associated problems.