Ensemble equivalence for general many-body systems

TL;DR

This paper demonstrates that the equivalence of different statistical ensembles, like microcanonical and canonical, is a universal principle applicable to all many-body systems with definable equilibrium states, extending previous mean-field results.

Contribution

It generalizes the ensemble equivalence principle from specific mean-field models to all many-body systems with well-defined equilibrium states.

Findings

Ensemble equivalence is a universal property of many-body systems.

Concavity of entropy determines ensemble equivalence.

The result applies to various dual ensembles like canonical and grand-canonical.

Abstract

It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e., whether they give rise to the same equilibrium states. Here we show that this correspondence is actually a general result of statistical mechanics: it holds for any many-body system for which equilibrium states can be defined and in principle calculated. The same correspondence applies for other dual statistical ensembles, such as the canonical and grand-canonical ensembles.