A framework for the use of generative modelling in non-equilibrium statistical mechanics

TL;DR

This paper introduces a generative modelling framework based on the variational free energy principle for understanding and representing the dynamics of non-equilibrium, self-organising systems, providing a tractable and unified statistical approach.

Contribution

It proposes a novel use of generative models and the variational free energy principle to model coupled, non-equilibrium systems, offering a new theoretical perspective.

Findings

Provides a variational inference interpretation of system dynamics

Offers a parsimonious explanation of system evolution based on coupling properties

Enables construction of nested models respecting subsystem relations

Abstract

We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad class includes open or non-equilibrium systems and is especially relevant to self-organising systems. The ensuing variational free energy principle (FEP) has certain advantages over using random dynamical systems explicitly, notably, by being more tractable and offering a parsimonious explanation of why the joint system evolves in the way that it does, based on the properties of the coupling between system components. The FEP is a method whose use allows us to build a model of the dynamics of an object as if it were a process of variational inference, because variational free energy (or surprisal) is a Lyapunov function for its dynamics. In short, we argue that using generative models to represent and track relations amongst subsystems leads us to a particular statistical theory of interacting systems. Conversely, this theory enables us to construct nested models that respect the known relations amongst subsystems. We point out that the fact that a physical object conforms to the FEP does not necessarily imply that this object performs inference in the literal sense; rather, it is a useful explanatory fiction which replaces the `explicit' dynamics of the object with an `implicit' flow on free energy gradients -- a fiction that may or may not be entertained by the object itself.