Knitting a Markov blanket is hard when you are out-of-equilibrium: two examples in canonical nonequilibrium models

TL;DR

This paper investigates the difficulty of identifying Markov blankets in nonequilibrium systems, showing that sparse connectivity does not guarantee their presence and that systems further from equilibrium are less likely to have Markov blankets.

Contribution

It provides the first detailed analysis of Markov blankets in two canonical nonequilibrium models, challenging assumptions about their prevalence in living systems.

Findings

Sparse connectivity does not ensure Markov blankets in nonequilibrium steady states.

The more a system is out of equilibrium, the less likely it is to exhibit a Markov blanket.

Markov blankets are less common in systems further from equilibrium.

Abstract

Bayesian theories of biological and brain function speculate that Markov blankets (a conditional independence separating a system from external states) play a key role for facilitating inference-like behaviour in living systems. Although it has been suggested that Markov blankets are commonplace in sparsely connected, nonequilibrium complex systems, this has not been studied in detail. Here, we show in two different examples (a pair of coupled Lorenz systems and a nonequilibrium Ising model) that sparse connectivity does not guarantee Markov blankets in the steady-state density of nonequilibrium systems. Conversely, in the nonequilibrium Ising model explored, the more distant from equilibrium the system appears to be correlated with the distance from displaying a Markov blanket. These result suggests that further assumptions might be needed in order to assume the presence of Markov blankets in the kind of nonequilibrium processes describing the activity of living systems.