Entropy-Induced Collapse (EIC) Model – Part B: Mathematical Foundations of Quantum Collapse Threshold and Non-Markovian Dynamics

Entropy-Induced Collapse (EIC) Model – Part B: Mathematical Foundations of Quantum Collapse Threshold and Non-Markovian Dynamics Part B of the Entropy-Induced Collapse (EIC) Model series rigorously develops the mathematical foundation of the hypothesis introduced in Part A—that quantum wavefunction collapse is triggered by environmental entropy surpassing a dynamically evolving critical threshold S_{\mathrm{crit}}(t). We explicitly formalize the threshold, decomposing it into three physically motivated components: a baseline entropy S_0, a quantum error correction (QEC)-induced shift \delta(d), and entropy fluctuations modeled via fractional Brownian motion (fBm) to realistically represent non-Markovian environmental noise. Furthermore, we derive and analyze the associated nonlinear Lindblad equation describing entropy-driven collapse dynamics, ensuring compliance with fundamental constraints such as trace preservation, positivity, and no-signaling conditions. This theoretical framework provides clear mathematical definitions, parameter ranges, and predictive equations, establishing a robust platform for numerical simulations (Part C) and experimental validations (Part D). Ultimately, the EIC model aims to offer a physically grounded, experimentally accessible mechanism bridging quantum measurement, thermodynamics, and the emergence of classical irreversibility. Keywords: Quantum Measurement, Entropy-Induced Collapse, Quantum Error Correction, Fractional Brownian Motion, Non-Markovian Dynamics, Nonlinear Lindblad Equation, Quantum Thermodynamics, Wavefunction Collapse Publication Date: April 20, 2025 Author: Takao Koizumi, Independent Researcher, Japan Contact: [email protected] Related Works: Koizumi, T. (2025). Entropy-Induced Collapse (EIC) Model – Part A: A Thermodynamic Trigger for Quantum Measurement and the Arrow of Time. Zenodo. doi:10.5281/zenodo.15242310