Bayesian mechanics of self-organising systems

Abstract: Bayesian mechanics provides a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, elucidating the requisite generative models is essential for empirical applications to realistic self-organising systems. This work shows that the Hamiltonian of generic dynamical systems constitutes a class of generative models, thus rendering their Helmholtz energy equivalent to variational free energy under the identified generative model. The self-organisation that minimises the Helmholtz energy entails matching the system's Hamiltonian with that of the environment, leading to the ensuing emergence of their generalised synchrony. In essence, these self-organising systems can be read as performing variational Bayesian inference of their interacting environment. These properties have been demonstrated using coupled oscillators, simulated and living neural networks, and quantum computers. This framework offers foundational characterisations and predictions regarding asymptotic properties of self-organising systems interacting with their environment, providing insights into potential mechanisms underlying the emergence of intelligence.