Conservative Motion Theory – P III: Quantum Information Continuity and the Entropic Fredholm Limit

Kawasaki, Hideyo

Published Nov 19, 2025• 0 citations

Abstract

We formulate the conservation of quantum information within the Conservative Motion Theory (CMT) as an Entropic Fredholm Limit. Quantum entropy S = -\operatorname{Tr}(\rho \log\rho) is represented as a Fredholm trace functional of reflection–positive operators, yielding an exact continuity law \frac{dS}{dt}=0 for closed systems. The analytic extension to open dynamics introduces an informational curvature term that encodes dissipative behavior and unifies thermodynamic irreversibility with Fredholm reflection continuity. This work establishes the physical branch of CMT–P by showing that information, entropy, energy, and charge conservation all arise from a single Fredholm trace identity.

DOI: 10.5281/zenodo.17644865

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