Nonconcave entropies from generalized canonical ensembles

TL;DR

This paper demonstrates that the Gaussian ensemble, a generalized canonical ensemble, can accurately compute nonconcave entropies in the mean-field Curie-Weiss-Potts spin model, addressing limitations of traditional methods.

Contribution

It introduces the use of the Gaussian ensemble to calculate nonconcave entropies, providing a practical solution for models with nonconcave entropy functions.

Findings

Nonconcave entropy of the Curie-Weiss-Potts model is obtainable via the Gaussian ensemble.

The generalized canonical ensemble can overcome Legendre transform limitations.

Direct calculations confirm the effectiveness of the Gaussian ensemble for nonconcave entropies.

Abstract

It is well-known that the entropy of the microcanonical ensemble cannot be calculated as the Legendre transform of the canonical free energy when the entropy is nonconcave. To circumvent this problem, a generalization of the canonical ensemble which allows for the calculation of nonconcave entropies was recently proposed. Here, we study the mean-field Curie-Weiss-Potts spin model and show, by direct calculations, that the nonconcave entropy of this model can be obtained by using a specific instance of the generalized canonical ensemble known as the Gaussian ensemble.