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The study aims to establish a rigorous variational principle on statistical manifolds using the Fisher information metric.

December 30, 2025Open Access

Information Geometry and the Variational Structure of Physical Dynamics: A Rigorous Foundation

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The study aims to establish a rigorous variational principle on statistical manifolds using the Fisher information metric.
Proved uniqueness of the Fisher metric up to scaling based on seven axioms of distinguishability.
Demonstrated consistency with dynamical systems across various fields using geodesic motion.
Provided theoretical contributions including predictions on quantum decoherence and evolutionary limits.
Established that the Fisher metric is the unique Riemannian structure fulfilling the specified axioms.
Showed that familiar dynamical equations, like the Euler-Lagrange, can be derived from the framework.
Predicted bounds on quantum decoherence rates and limitations on evolutionary processes.

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Theoretical framework reveals unification of physics and machine learning through information geometry.

Anthony L Perry (2025) studied this question.

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