Quantum-Statistical Correspondences in Non-Local Operators: Entanglement, Phase Transitions, and Information Geometry

This record contains a preprint of the manuscript “Quantum-Statistical Correspondences in Non-Local Operators: Entanglement, Phase Transitions, and Information Geometry.” The paper develops a rigorous operator-theoretic and thermodynamic framework for non-local linear operators by embedding them into finite-temperature quantum statistical systems. The construction yields exact softmax–Gibbs correspondences, a characterization of operator expressivity via entanglement scaling, and a mean-field description of phase transitions and spectral statistics under coherent mixing. The manuscript has been submitted to the Journal of Mathematical Physics (AIP Publishing) and is currently under peer review. This Zenodo version is provided to establish a timestamped public preprint and DOI prior to formal peer review.