Methods for calculating nonconcave entropies

TL;DR

This paper reviews and compares five analytical methods for calculating nonconcave entropies in thermodynamics, using a long-range spin model as an illustrative example.

Contribution

It introduces and evaluates five distinct techniques for analytically determining nonconcave entropies, expanding tools available for thermodynamic analysis.

Findings

All five methods successfully compute nonconcave entropies.

The methods show consistent results on the long-range spin model.

Each method offers unique advantages depending on the context.

Abstract

Five different methods which can be used to analytically calculate entropies that are nonconcave as functions of the energy in the thermodynamic limit are discussed and compared. The five methods are based on the following ideas and techniques: i) microcanonical contraction, ii) metastable branches of the free energy, iii) generalized canonical ensembles with specific illustrations involving the so-called Gaussian and Betrag ensembles, iv) restricted canonical ensemble, and v) inverse Laplace transform. A simple long-range spin model having a nonconcave entropy is used to illustrate each method.