The second law of Thermodynamics as a theorem in quantum mechanics

TL;DR

This paper rigorously proves the Minimum Work Principle in quantum thermodynamics for systems starting from pure states with energy concentration, modeling adiabatic processes with time-dependent Hamiltonians.

Contribution

It establishes a rigorous proof of the Minimum Work Principle for quantum systems undergoing adiabatic operations, extending thermodynamic principles to quantum regimes.

Findings

Minimum Work Principle holds for almost all waiting times.

The proof applies to pure initial states with energy concentration.

The model simulates adiabatic thermodynamic operations in quantum systems.

Abstract

We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly concentrated at a single value, we consider a time evolution determined by a time-dependent Hamiltonian as a model of an adiabatic operation in thermodynamics. We take a family of operations with the same procedure and various ``waiting times.'' Then the Minimum Work Principle is rigorously proved for almost all choices of the waiting time.