Ensemble inequivalence, bicritical points and azeotropy for generalized Fofonoff flows

TL;DR

This paper provides a theoretical framework for understanding equilibrium states in 2D and geophysical flows, revealing ensemble inequivalence, phase transition criteria based on domain geometry, and novel phenomena like bicritical points and azeotropy.

Contribution

It introduces explicit computations of ensemble inequivalence and phase transition criteria that depend solely on domain geometry, and reports the first examples of bicritical points and azeotropy in long-range interacting systems.

Findings

Explicit criteria for phase transition locations and types.

First demonstration of ensemble inequivalence and negative specific heat in these models.

Identification of bicritical points and azeotropy phenomena.

Abstract

We present a theoretical description for the equilibrium states of a large class of models of two-dimensional and geophysical flows, in arbitrary domains. We account for the existence of ensemble inequivalence and negative specific heat in those models, for the first time using explicit computations. We give exact theoretical computation of a criteria to determine phase transition location and type. Strikingly, this criteria does not depend on the model, but only on the domain geometry. We report the first example of bicritical points and second order azeotropy in the context of systems with long range interactions.