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March 26, 2026Open Access

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

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Authors

APAnthony L Perry

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Overview

Rigorous principle reveals structural unity in physics, indicating new predictions and methodologies.

Key Points

  • The aim is to establish a rigorous variational principle on statistical manifolds using the Fisher information metric.
  • Developed axioms for distinguishability between probability distributions;
  • Proved uniqueness of the Fisher metric through Chentsov's theorem;
  • Demonstrated recovery of equations of motion across various physical frameworks.
  • Uniqueness of the Fisher metric proved under seven axioms;
  • Introduced seven novel predictions including scaling laws for quantum processes and neural networks;
  • Established explicit criteria for falsification and addressed potential criticisms.

Cite This Study

Anthony L Perry (2026) studied this question.

synapsesocial.com/papers/6a3ed431901a52dbcb715af2https://doi.org/10.5281/zenodo.18102165
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Also Consider

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  1. 1Information Geometry and the Variational Structure of Physical Dynamics: A Rigorous Foundation2026
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  4. 4Information-Geometry Equivalence (IGE): A Unified Framework for Reconciling General Relativity and Quantum Mechanics Through Quantum Fisher Information2026
  5. 5Information as Matter in Infinite Dimensions Fisher Geometry, Information Ricci Flow, and a Unified Field Framework2026