  Bayesian mechanics is a framework that addresses dynamical systems that can
be conceptualised as Bayesian inference. However, the elucidation of requisite
generative models is required 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 naturally 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 an ensuing emergence of their generalised synchrony. In
short, these self-organising systems can be read as performing variational
Bayesian inference of the interacting environment. These properties have been
demonstrated with coupled oscillators, simulated and living neural networks,
and quantum computers. This notion offers foundational characterisations and
predictions regarding asymptotic properties of self-organising systems
exchanging with the environment, providing insights into potential mechanisms
underlying emergence of intelligence.
