Entropy-Induced Collapse (EIC) Model – Part (1) A Deterministic-Stochastic Framework Integrating Quantum Error Correction and Non-Markovian Dynamics

This paper presents Part 1 of the Entropy-Induced Collapse (EIC) Model, a deterministic-stochastic theoretical framework that describes quantum wavefunction collapse as triggered when the environmental entropy S(t) surpasses a dynamically evolving critical threshold S_{\text{crit}}(t). The model integrates Quantum Error Correction (QEC) and realistic non-Markovian noise characterized by fractional Brownian motion (fBm), distinguishing itself from conventional collapse theories such as GRW and CSL by accurately predicting experimental coherence times observed in superconducting qubit systems implementing surface-code QEC protocols. The paper includes detailed mathematical derivations, numerical simulations, statistical and systematic error analyses, and explicitly proposed experimental protocols tailored for superconducting and trapped-ion quantum platforms. It bridges fundamental quantum measurement theory with experimentally accessible quantum-information technology, providing a rigorous and testable foundation for future theoretical and empirical validations. Note for LaTeX Users: This manuscript was originally written in a Japanese text environment, resulting in Yen symbols (¥) in place of standard LaTeX backslashes (\). Users intending to compile or use the equations should replace all instances of ‘¥’ with ‘\’ to properly format LaTeX mathematical expressions. Important clarification regarding previous publications: All previous papers in this series (including the paper dated March 8, 2025) were unintentionally reduced by more than half of their original content due to automated AI summarization. Users are advised to refer to this current manuscript as the authoritative and complete version of the EIC model. Ethical Statement: This research is explicitly intended for peaceful purposes and should be used exclusively for the benefit of humanity.