A Free Energy Principle for a Particular Physics

Abstract

This monograph attempts a theory of every ‘thing’ that can be distinguished from other ‘things’ in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales.

These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every ‘thing’, its main contribution is to examine the implications of Markov blankets for selforganisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states.

Introduction

Our starting point is a definition of things in terms of systems that possess an invariant measure; namely, weakly mixing systems that possess an attracting set. The description of such systems usually starts using the formalism of random dynamical systems; for example, the flow or dynamics of systemic states based on random differential equations (e.g., a Langevin equation). This is where the current treatment starts – and then stops. It stops by asking some obvious questions; like, what are states and where do random fluctuations come from? These questions lead to even simpler questions; namely, if we are dealing with the states of something, what is the thing that possesses those states – and how does one distinguish anything from something else?

An invariant measure is necessary for a being to exist. (The observer's relationship to self, e.g.)

To address the nature of things, we start by asking how something can be distinguished from everything else. [...] we will call on the notion of conditional independence as the basis of this separation. [W]e assume that for something to exist it must possess (internal or intrinsic) states that can be separated statistically from (external or extrinsic) states that do not constitute the thing.

later on, pg 25:

To explain this kind of dynamical behaviour, it has been suggested that some random dynamical systems are attracted to critical points.

Yes: organisms must be attracted to the critical point of reproduction!