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December 19, 2025Open Access

The Fisher Information Action for Quantum Dynamics

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Authors

JJJesper Lyng Jensen

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Overview

Variational framework yields nonlinear Schrödinger equation in quantum dynamics, indicating new insights into information geometry.

Key Points

  • This work aims to connect quantum mechanics with information-theoretic principles using Fisher-information geometry.
  • Developed a Lorentz-invariant variational framework.
  • Introduced an action functional based on Madelung representation.
  • Derived a modified Klein–Gordon equation with nonlinear terms.
  • Established a link between Fisher-information curvature and quantum dynamics.
  • Obtained a nonlinear Schrödinger equation with Fisher information as a corrective term.
  • Demonstrated distinctive characteristics for future experimental verification.

Cite This Study

Jesper Lyng Jensen (2025) studied this question.

synapsesocial.com/papers/69449a922f0218eca95085dahttps://doi.org/10.20944/preprints202512.1400.v1
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  5. 5Information Geometry and the Variational Structure of Physical Dynamics: A Rigorous Foundation2025