Approach to Equilibrium in Translation-Invariant Quantum Systems: Some Structural Results

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 in entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase in 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.

Automated summary

This study investigates the problem of approaching equilibrium in algebraic quantum statistical mechanics, focusing on the relationship between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy). The main finding is that approaching equilibrium necessarily leads to a strict increase in specific (mean) energy and entropy. Furthermore, the concept of quantum weak Gibbs state is introduced and is of independent interest.