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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Mother Equation and the Free Energy Principle A Term-by-Term Comparison of Two Fokker-Planck Frameworks

Authors: Schmieke, Marcus;

The Mother Equation and the Free Energy Principle A Term-by-Term Comparison of Two Fokker-Planck Frameworks

Abstract

The Quantum Blueprint Formalism (QBF) and Karl Friston’s Free Energy Principle (FEP) both derive Fokker-Planck dynamics from structural conditions. This paper performs the first explicit term-by-term mapping between the two frameworks. The QBF’s Mother Equation and the FEP’s Langevin dynamics are shown to be the same equation with different decompositions, different constraints, and different interpretations. The reversible sectors are identical: the QBF’s tension functional Φ equals the FEP’s surprisal (up to a factor Dₛ), and the equilibrium distributions coincide. The irreversible sectors differ in one structural point: the QBF constrains the solenoidal (divergence-free) flow via the symplectic form ωI (from non-commutativity), while the FEP leaves the solenoidal component as a free antisymmetric matrix Q. This difference produces a testable prediction: in the QBF, the solenoidal flow is Hamiltonian (generated by a symplectic form applied to the gradient of the potential); in the FEP, it can be any divergence-free field. Measuring whether biological solenoidal flows are consistently Hamiltonian would discriminate between the two frameworks at the biological level, without requiring the QBF’s full derivation of spacetime. Five points of agreement and three points of disagreement are identified. The frameworks are nested: the FEP is the restriction of the Mother Equation to systems that already possess spacetime and a Markov blanket.

Keywords

Quantum physics, Friston

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
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