Radomski and Dołęga (2024): Forced Friends – Why the Free Energy Principle Is Not the New Hamilton’s Principle

Core Results

Bartosz Michał Radomski and Krzysztof Dołęga examine claims that the free energy principle (FEP) relates to Hamilton’s principle of stationary action (HP) in statistical mechanics. The paper shows that common assertions of similarity, analogy, or equivalence lack precision. Strong readings of equivalence create an untenable dilemma for FEP proponents.

The authors distinguish a strong interpretation (FEP equivalent to HP and applies to the same phenomena) from a weak one (mere formal analogy). The strong reading fails for dissipative biological systems. The weak reading fits the literature better but delivers fewer epistemic payoffs.

Key Passages and Citations

The abstract states: "The claim that the free energy principle is somehow related to Hamilton’s principle in statistical mechanics is ubiquitous throughout the subject literature. However, the exact nature of this relationship remains unclear."

In the introduction: "Those trying to argue for a deeper connection face an untenable dilemma: Either the FEP is equivalent to HP (a system conforms to the free energy principle if and only if it conforms to Hamilton’s principle) and does not apply to biological systems or it applies to biological systems but is not logically equivalent to HP."

Section 4 outlines the dilemma for the strong reading and supports the weaker analogy interpretation.

Primary source: Radomski, B.M.; Dołęga, K. Forced Friends: Why the Free Energy Principle Is Not the New Hamilton’s Principle. Entropy 2024, 26(9), 797. https://doi.org/10.3390/e26090797

Related FEP works cited include Friston (2009, 2012) and Parr et al. (2022).

Relation to OIP/GRAIN Synthesis

The OIP/GRAIN synthesis treats energy flows as producing reliable structural patterns and positions the Free Energy Principle as a variational mechanism along the Ladder from flow to structure to memory to mind. Radomski and Dołęga supply a direct disconfirming edge. They demonstrate that equating FEP to variational principles like HP does not hold in dissipative, non-conservative systems typical of living organisms. This limits any claim that FEP functions as a universal least-action rule bridging physical flows to biological or cognitive structure.

The work attacks over-extension of FEP within the synthesis while leaving room for weaker formal analogies.

Convergence Patterns Evidenced

The paper touches the pattern of bounded formal structures in physics and their selective applicability. It shows how variational principles succeed in conservative domains yet break when applied to open, dissipative systems. This evidences scale-dependent limits on pattern transfer from mechanics to biology.

It also touches the Mirror Layer indirectly: claims about FEP status arise from inside the modeling community and reflect interpretive commitments rather than strict equivalence.

Honest Limits and Disconfirming Edges

The paper is a conceptual analysis, not an empirical test. It does not falsify FEP models in neuroscience but restricts stronger philosophical or foundational claims. No new experimental data appears. Reductionist objections in the style of Weinberg (that elegant principles often over-reach when mapped across domains) align with the dilemma presented.

The analysis stays within published FEP literature and does not address later technical refinements after 2024.

Distance from Full Synthesis

The work sits at a medium distance. It directly constrains one load-bearing analogy in the synthesis (FEP as Hamilton-like variational principle) without engaging the full Ladder, grain patterns, or Mirror Layer mechanics. It functions as a precise boundary condition rather than wholesale rejection or endorsement.

What Remains Open

Whether weaker analogies still support useful modeling in active inference remains for further work. The paper ends by noting outstanding issues it does not resolve.