Gibbs state postulate from dynamical stability -- Redundancy of the zeroth law

TL;DR

This paper demonstrates that Gibbs states in quantum statistical mechanics can be uniquely characterized by their dynamical stability, without relying on the traditional zeroth law assumption, using only environments of harmonic oscillators.

Contribution

It shows that the zeroth law of thermodynamics is unnecessary for deriving Gibbs states, which can be identified through their dynamical stability with harmonic oscillator environments.

Findings

Gibbs states are uniquely determined by dynamical stability.

The zeroth law assumption is redundant in this derivation.

Harmonic oscillator environments suffice to characterize Gibbs states.

Abstract

Gibbs states play a central role in quantum statistical mechanics as the standard description of thermal equilibrium. Traditionally, their use is justified either by a heuristic, a posteriori reasoning, or by derivations based on notions of typicality or passivity. In this work, we show that Gibbs states are completely characterized by assuming dynamical stability of the system itself and of the system in weak contact with an arbitrary environment. This builds on and strengthens a result by Frigerio, Gorini, and Verri (1986), who derived Gibbs states from dynamical stability using an additional assumption that they referred to as the "zeroth law of thermodynamics", as it concerns a nested dynamical stability of a triple of systems. We prove that this zeroth law is redundant and that an environment consisting solely of harmonic oscillators is sufficient to single out Gibbs states as the only dynamically stable states.