Entropy-Induced Collapse (EIC): A Deterministic-Stochastic Framework Integrating Quantum Error Correction and Non-Markovian Dynamics

This paper introduces the Entropy-Induced Collapse (EIC) model, a novel approach to wavefunction collapse based on entropy dynamics, fractal noise, and quantum error correction (QEC). The key hypothesis is that collapse occurs when the environmental von Neumann entropy S(t) exceeds a dynamically evolving threshold S_{\mathrm{crit}}(t), influenced by non-Markovian memory effects. Key Contributions: • Entropy-Driven Collapse: Collapse is defined as a deterministic-stochastic process governed by entropy fluctuations. • Fractal Noise and Non-Markovianity: The model incorporates fractional Brownian motion (fBm) to capture long-range correlations. • Quantum Error Correction (QEC): The impact of QEC on delaying collapse is explored through simulation data up to code distance d=11. • Experimental Roadmap: Proposed tests using superconducting qubits (IBM Quantum, Google Sycamore) and trapped ion systems. • Implications for Quantum Cryptography: Effects on quantum key distribution (QKD) security under non-Markovian noise are analyzed. This work aims to unify quantum foundations, quantum computing, and quantum information theory by providing a testable framework for entropy-induced collapse. Keywords: Wavefunction Collapse, Entropy, Fractal Noise, Quantum Error Correction, Quantum Computing, Quantum Cryptography, Non-Markovian Dynamics, QKD