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.