Threshold Dynamics and Entropy Stabilization in Quantum-to-Classical Transition Systems: A Dual-Parameter Analysis

The single-threshold model of the quantum-to-classical transition treats classicality as a binary crossing of a single Imass criterion. This paper argues that the transition is better described by a dual-parameter structure: a lower threshold α at which coherence becomes operationally negligible, and an upper threshold β at which classical distinguishability becomes stable against perturbation. The interval [α,β] constitutes a hysteresis gate within which the transition is directionally asymmetric — re-coherence remains possible below β but is operationally suppressed beyond it. A spectral decomposition of informational mass (Imass) is introduced, resolving the total accumulated environmental distinguishability into mode-resolved contributions. This decomposition enables precise characterisation of entropy plateau conditions: regions of near-zero entropy growth arising when dominant spectral modes have saturated while subdominant modes continue accumulating slowly. As a derived consequence of the dual-threshold structure, the framework predicts Mpemba-like trajectory crossings between systems initialised at different Imass values. A system with higher initial Imass can exhibit lower entropy than a system with lower initial Imass at intermediate times, owing to earlier entry into the entropy plateau regime. This prediction is mechanistically distinct from existing quantum Mpemba results and constitutes a testable consequence of the framework. A minimal three-level qutrit Lindblad model is developed to illustrate the dynamics numerically.