2025/08/20 by Rohit Kishan Ray, Ray, Rohit Kishan
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2508.14389
openalex publication_date 2025/08/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
The Steepest Entropy Ascent (SEA) ansatz, recently recognized as the fourth law of thermodynamics, governs the irreversible evolution of a system from a non-equilibrium state toward a unique maximum-entropy equilibrium. SEA builds upon the second law to unify mechanics and thermodynamics. Due to its nonlinear nature, exact solutions to the SEA equation of motion are scarce. To address this, the Fixed Lagrange Multiplier (FLM) method is developed as an approximate analytical tool, applicable to both two-level and higher-dimensional quantum systems. Using quantum walks, a universal computation model, the study applies FLM to analyze and solve the SEA dynamics for single-component N-level systems. The approximate FLM solutions show strong agreement with full numerical simulations, particularly in regions of maximum entropy production consistent with SEA predictions. To extend SEA analysis to composite systems, especially two-qubit systems, the work provides a general framework for N-level Bloch vector parametrization. It includes analytical roots for N=3 and a complete parametrization for N=4, along with a method for analytically computing operator traces in this representation. Finally, the study examines the no-signaling condition in nonlinear quantum theories. While nonlinearity often implies faster-than-light signaling, the SEA framework inherently respects no-signaling. The equation of motion for both separable and entangled (e.g., Bell-diagonal) composites confirms that SEA maintains locality and provides a robust foundation for modeling decoherence in both open and closed quantum systems. (Abridged for ArXiv)