An approach to non-equilibrium statistical physics using variational Bayesian inference (2406.11630v1)

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. Using the FEP allows us to model 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 among 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 among 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.

• The paper introduces a unified framework that applies variational Bayesian inference to explain non-equilibrium system dynamics.
• It employs generative models with Markov blankets to partition states and optimize free energy gradients for system adaptation.
• The approach offers new insights into self-organization by framing system dynamics as an approximate Bayesian inference process.

An Approach to Non-Equilibrium Statistical Physics Using Variational Bayesian Inference

The paper "An approach to non-equilibrium statistical physics using variational Bayesian inference" introduces a comprehensive framework for understanding the dynamics of non-equilibrium systems, particularly self-organizing systems, through the lens of Bayesian inference. The authors, Maxwell J D Ramstead, Dalton A R Sakthivadivel, and Karl J Friston, explore the utility of generative models in describing the dependencies between states or trajectories of system components and articulate how the Free Energy Principle (FEP) offers a parsimonious explanation for the evolution of such systems.

Overview and Contribution

The paper makes a significant theoretical contribution by proposing that systems characterized by interacting components can be efficiently modeled using generative models, and specifically, through processes akin to variational Bayesian inference. The authors take the stance that the FEP, rather than formalizing the literal computation of inference by physical systems, serves as an "explanatory fiction." That is, it replaces the explicit dynamics of couples systems with an implicit flow on free energy gradients. This conceptualization allows the dynamics within a system to be interpreted as optimizing processes that mimic inference on environmental states.

Mathematical Formulation

The paper notably focuses on the role of the Markov blanket—a concept crucial for studying dependencies within probabilistic graphical models and effective in defining system boundaries in statistical physics. The generative models incorporate Markov blankets to delineate internal, external, and boundary states, leading to a rich representation of system dynamics under the assumption of particular partitions. The authors elucidate how internal states can be aligned with a form of variational inference aimed at reducing free energy, thereby maintaining system integrity in non-equilibrium settings.

Implications

Several key implications arise from the authors’ examination of the FEP within non-equilibrium statistical physics:

1. Modeling Dynamical Systems: Utilizing the FEP permits the abstraction of the dynamics of an internally consistent and coherently bounded system as a gradient descent on free energy. This process enables the inference of statistical properties of its environment, providing a bridge between thermodynamic principles and inferential mechanisms.
2. Self-Organization and Adaptation: The treatment of systems as approximate Bayesian inferencers lends insights into phenomena like adaptation and morphogenesis, where complex behavior emerges from simple inferential rules encoded within the system's structure.
3. Critique and Scope: The authors address critical commentary regarding the FEP’s potential to conflate system dynamics with inference, indicating that rather than constituting a model reification error, this conflation is a designed feature of a scientific model. By constructing generative models indicative of system-environment relations, the work exemplifies how systems track environmental changes without necessarily literalizing inference.

Future Speculation

The authors' approach opens avenues for extending the FEP into multiple domains beyond theoretical physics, particularly into cognitive sciences and systems biology. By grounding its principles within such diverse fields, future research might explore how optimal predictive coding strategies operate across natural and artificial systems. Moreover, such understanding may refine computational models simulating consciousness and perception.

In conclusion, the paper proposes a robust interpretative and mathematical framework under the FEP umbrella, potentially reshaping how researchers approach non-equilibrium statistical physics and related domains. The combination of generative models and inference akin representations holds promise for future exploration into the theoretical and practical modeling of complex adaptive systems.