Nonconcave entropies from generalized canonical ensembles

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.

5 pages, RevTeX4, 3 figures (best viewed in ps)

References in corpus (13)

• Negative Specific Heat in Astronomy, Physics and Chemistry
• Inequivalence of ensembles in a system with long range interactions
• Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models
• An Introduction to the Thermodynamic and Macrostate Levels of Nonequivalent Ensembles
• Large deviation techniques applied to systems with long-range interactions
• Gravitational instability of isothermal and polytropic spheres
• On first-order phase transition in microcanonical and canonical non-extensive systems
• Thermodynamic versus statistical nonequivalence of ensembles for the mean-field Blume-Emery-Griffiths model
• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• Generalized canonical ensembles and ensemble equivalence
• The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble
• Phase diagram of self-attracting systems
• Metastability within the generalized canonical ensemble

Cited by in corpus (7)

• Negative magnetic susceptibility and nonequivalent ensembles for the mean-field ${\varphi }^4$ spin model
• Extended gaussian ensemble solution and tricritical points of a system with long-range interactions
• The thermodynamic limit and black hole entropy in the area ensemble
• Methods for calculating nonconcave entropies
• Asymptotic equivalence of probability measures and stochastic processes
• The extended gaussian ensemble and metastabilities in the Blume-Capel model
• Global optimization, the Gaussian ensemble, and universal ensemble equivalence