Interaction, Stabilization, and Entanglement: A Persistence-Field Interpretation with Open-System Corrections

This work develops a persistence-field framework for interpreting quantum correlations, entanglement, and measurement without invoking nonlocal collapse. We model quantum systems as complex scalar persistence fields whose conservative sector reduces exactly to the linear Schrödinger equation, while decoherence emerges from structured gain–loss imbalance rather than wavefunction discontinuity. Within this formulation: Entanglement is interpreted as phase-locked persistence structure across coupled subsystems. Measurement is described as leakage-induced phase decoherence. Decoherence rates arise from imbalance parameters rather than ad hoc collapse postulates. We derive a PTL-induced decoherence correction for a two-level entangled system and show that standard quantum predictions are recovered in the conservative limit. The framework does not modify quantum mechanics in isolated systems but provides a structured interpretation for open-system dynamics and decoherence processes. The theory yields falsifiable predictions concerning decoherence scaling under controlled gain–loss asymmetry and proposes experimental regimes where deviations from purely environmental decoherence models may be observable. This manuscript is part of a multi-paper program developing a nonlinear complex scalar persistence-field framework for quantum and classical stability phenomena.