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

TL;DR

This paper derives the second law of thermodynamics from quantum statistical mechanics for macroscopic systems using a hybrid quantum approach, demonstrating entropy increase and fundamental principles.

Contribution

It provides a rigorous quantum mechanical derivation of the second law for macroscopic systems in a realistic hybrid setting, including autonomous evolution.

Findings

Proves Planck's and Kelvin's principles in a quantum framework

Demonstrates entropy increase in a hybrid quantum system

Establishes a general derivation applicable to realistic macroscopic systems

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.