Quantum statistical mechanical derivation of the second law of thermodynamics: a hybrid setting approach

Abstract

Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic systems. Although the main body of the article is self-contained there are two supplemental notes on closely related topics, namely, the law of entropy increase and the approach based on a unital time-evolution.

18 pages, 2 figures, the final version which will appear in Phys. Rev. Lett. A drastic revision has been made since the previous version (even the title has changed). There are two supplemental notes

References in corpus (6)

• Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
• Clock-Driven Quantum Thermal Engines
• Measurement-based Formulation of Quantum Heat Engine
• Reexamination of Pure Qubit Work Extraction
• From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview
• The second law of thermodynamics for pure quantum states

Cited by in corpus (13)

• The role of coherence in the non-equilibrium thermodynamics of quantum systems
• Universal Coherence-Induced Power Losses of Quantum Heat Engines in Linear Response
• Uncertainty relations in implementation of unitary operations
• Efficiency versus Speed in Quantum Heat Engines: Rigorous Constraint from Lieb-Robinson Bound
• Coherence cost for violating conservation laws
• Quantum Thermodynamics and Quantum Coherence Engines
• Universal limitations on implementing resourceful unitary evolutions
• Quantum Jarzynski equality of measurement-based work extraction
• Thermodynamic Reverse Bounds for General Open Quantum Processes
• Macrostate equivalence of two general ensembles and specific relative entropies
• Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes
• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution
• Extensive increase of entropy in quantum quench