Approach to equilibrium in translation-invariant quantum systems: some structural results

TL;DR

This paper investigates how quantum systems approach equilibrium, establishing that such an approach involves a strict increase in energy and entropy, and introduces the concept of quantum weak Gibbs states.

Contribution

It provides structural results linking the approach to equilibrium with entropy and energy increase, and introduces the quantum weak Gibbs state concept.

Findings

Approach to equilibrium requires strict energy and entropy increase.

The concept of quantum weak Gibbs state is introduced and analyzed.

Structural relations between thermodynamic laws are established.

Abstract

We formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase of entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase of the specific (mean) energy and entropy. In the course of our analysis, we introduce the concept of quantum weak Gibbs state which is of independent interest.