A Bayesian mechanics for adaptive systems

We develop a Bayesian mechanics for adaptive systems. This mechanics has the same starting point as quantum, statistical and classical mechanics. The only difference is that careful attention is paid to the way that the states internal to something interface with the states external to it.

 

We model adaptive systems as coupled stochastic processes at non-equilibrium steady state, which describe the interaction between external, internal, sensory and active states of a particle. We unpack the consequences of this in terms of approximate Bayesian inference, in the sense that internal states can be seen as continuously inferring external states, consistently with variational inference in Bayesian statistics and theoretical neuroscience.

 

Beyond this, we single out an interesting sort of non-equilibrium steady-state reminiscent of biological systems, wherein the states of a particle have low entropy fluctuations. Their trajectories can be governed by a variational principle of least action over a functional relating to optimal Bayesian design and decision-making. We conclude with simulations ranging from a primordial soup to a Human arm movement, distinguishing between various sorts of non-equilibrium steady states.