Thermalization and irreversibility of an isolated quantum system II

2025/06/02 by Guo, Xue-Yi
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2506.01351

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The irreversible entropy increase described by the second law of thermodynamics is fundamentally tied to thermalization and the emergence of equilibrium. In the first part of our work (Ref: arXiv.2503.04152), we constructed an isolated gas system model and numerically demonstrated irreversible growth of entanglement entropy caused by erasure of spread non-equilibrium state information. Here, we mathematically prove that for a typical macroscopic system in a non-equilibrium state |ϕ₀⟩, the quantum state |ϕ'₀⟩ = O(t)|ϕ₀⟩ will inevitably evolve toward equilibrium. Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective. From this perspective, the second law can be stated as: In typical macroscopic physical systems, the spreading and erasure of non-equilibrium information is inevitable.

Citations

• Macroscopic thermalization by unitary time-evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Teufel-Tumulka-Vogel theorem
• Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system
• Circuit complexity and functionality: a thermodynamic perspective
• Typical Macroscopic Long-Time Behavior for Random Hamiltonians
• Quantum entropy thermalization
• Eigenstate thermalization hypothesis
• Towards local equilibration in closed interacting quantum many-body systems
• From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
• Physical Cost of Erasing Quantum Correlation
• Decoherence, einselection, and the quantum origins of the classical
• Chaos and Quantum Thermalization
• Quantum statistical mechanics in a closed system
• Stability of quantum motion in chaotic and regular systems

Related

• Emergence of a second law of thermodynamics in isolated quantum systems
• Thermalization and irreversibility of an isolated quantum system
• Entropy: An inherent, nonstatistical property of any system in any state
• Improved Landauer's principle and generalized second law of thermodynamics with initial correlations and non-equilibrium surrounding environments
• Numerical analysis of second law of thermodynamics and irreversibility in exemplary quantum systems