Yes, like the association of physical entropy with information and the association of Shannon information with physics, it is an analogy. Analogy is a form of explanation. An analogy between a domain that is well understood and a novel or less well understood domain is perceived to be explanatory. 'Well understood" is relative to the expertise of the person enjoying the analogy.
The Andrews paper proposes that
… the FEP … designate[s] a model structure, to which philosophers and scientists add various construals, leading to a plethora of models based on the formal structure of the FEP. An entailment of this position is that demands placed on the FEP that it be falsifiable or that it conform to some degree of biological realism rest on a category error.
The FEP is a descriptive apparatus about models of behavior. PCT is a model of behavior. The FEP is not falsifiable and any conformity of the FEP apparatus to biological systems is ‘purely coincidental’ and in the imagination of the reader. (Works of fiction typically have this ‘purely coincidental’ disclaimer. If you infer from that an analogy, it is apt. Literary fiction, in a very different way, also provides valid insights with no claim to be the real thing.) PCT is falsifiable and has been countless times tested in ways capable of falsifying it, and a fundamental premise is that the control organization presented in a PCT model of behavior (the ‘white box’) predicts structures that are found or will be found in organisms that engage in the modeled behavior (the ‘black box’).
Comparing PCT and FEP directly to each other, in Andrews’s words, “rests on a category error.”
Martin Taylor was quite expert in the analytical point of view, like the point of view taken by the FEP. I recommend his magnum opus digging into the systemic consequences, corollaries, and ramifications of PCT, Powers of Perceptual Control. A raw draft is here. Martin’s ongoing revision process was interrupted by his death last March. A team of volunteers is editing it for publication. Martin thought that the FEP “seems to mesh very well with PCT, filling in with conscious control where PCT cannot suffice with non-conscious control, and providing a mathematical background that applies equally to both.”
You can also look for Martin’s (and Warren’s) posts about Friston, free energy, etc. in Discourse, including in the CSGnet archive (e.g. here results of a search on “mmt friston”). You will also find there sometimes quite sharp rejections of everything that Martin has said on the subject. Looking only at this prominent contention focusing on the analytical, systemic point of view (its merits or pointlessness) one might remain unaware of Martin’s understanding of PCT from the point of view of the control system, his training and deep experience in experimental psychology grounded in this understanding, and his invention and development of a way of modeling communication between autonomous control systems (Layered Protocol Theory, LPT) which he and Bill Powers recognized to be a subset of PCT.
These rejections rest on the same category error. From that point of view within PCT, it is beside the point, useless, and (it is claimed) even quite wrong, to talk about systemic properties of control systems with mathematical concepts and tools which apply with apparently great generality to all physical systems, such as information theory and (much more recently) the mathematics of crumpling and rattling ( Chvykov, P, Berrueta, T.A., Vardham, A., et al. 2021. “Low Rattling: A Predictive Principle for Self-organization in Active Collectives.” Science 371: 90-95. DOI:10.1126/science.abc6182.). You may encounter similar categorical rejection of what you have to say about the FEP for the same reason.