  In this commentary, we respond to a technical analysis of the Free Energy
Principle (hereafter: FEP) presented in "How particular is the physics of the
Free Energy Principle" by Aguilera et al. In the target article, the authors
analyzed certain sparsely coupled stochastic differential equations whose
non-equilibrium steady-state densities are claimed--in previous FEP
literature--to have a Markov blanket. The authors demonstrate that in general,
Markov blankets are not guaranteed to follow from sparse coupling. The current
commentary explains the relationship between sparse coupling and Markov
blankets in the case of Gaussian steady-state densities. We precisely derive
conditions under which causal coupling leads--or does not lead--to Markov
blankets. Importantly, our derivations hold for both linear and non-linear
stochastic differential equations. This result may shed light on the sorts of
systems which we expect to have Markov blankets. Future work should focus on
verifying whether these sorts of constraints are satisfied in realistic models
of sparsely coupled systems.
