Entropy-Induced Collapse (EIC): Quantum State Reduction Driven by Environmental Entropy and the Emergence of the Arrow of Time

This paper presents a rigorous formulation of the Entropy-Induced Collapse (EIC) model, a novel framework proposing that quantum wavefunction collapse is triggered when the environmental entropy surpasses a dynamically evolving threshold. By integrating non-Markovian noise modeled via fractional Brownian motion and accounting for the effects of quantum error correction (QEC), the model offers a thermodynamically grounded mechanism for state reduction. The approach introduces a nonlinear Lindblad master equation linking entropy gradients to collapse dynamics, providing a physically testable pathway to explain the quantum-to-classical transition. Experimental protocols using superconducting qubits, trapped ion systems, and precision force measurements are proposed. As Part A of the EIC Model Series, this work focuses strictly on physical principles and testable predictions, setting aside philosophical or cognitive interpretations for future studies.