Solvable phase diagrams and ensemble inequivalence for two-dimensional and geophysical turbulent flows

TL;DR

This paper analytically demonstrates ensemble inequivalence in two-dimensional and geophysical turbulent flows, revealing new mechanisms linked to phase transitions and the influence of domain geometry, topography, and interaction scales.

Contribution

It introduces two novel mechanisms for ensemble equivalence in turbulent flows related to phase transition phenomena, expanding understanding of flow topologies and statistical ensemble behavior.

Findings

Ensemble inequivalence occurs in a broad class of turbulent flow equilibria.

Two new mechanisms for ensemble equivalence are identified: second-order azeotropy and bicritical points.

Decreasing the Rossby radius of deformation widens the parameter range for ensemble inequivalence.

Abstract

Using explicit analytical computations, generic occurrence of inequivalence between two or more statistical ensembles is obtained for a large class of equilibrium states of two-dimensional and geophysical turbulent flows. The occurrence of statistical ensemble inequivalence is shown to be related to previously observed phase transitions in the equilibrium flow topology. We find in these turbulent flow equilibria, two mechanisms for the appearance of ensemble equivalences, that were not observed in any physical systems before. These mechanisms are associated respectively with second-order azeotropy (simultaneous appearance of two second-order phase transitions), and with bicritical points (bifurcation from a first-order to two second-order phase transition lines). The important roles of domain geometry, of topography, and of a screening length scale (the Rossby radius of deformation) are discussed. It is found that decreasing the screening length scale (making interactions more local) surprisingly widens the range of parameters associated with ensemble inequivalence. These results are then generalized to a larger class of models, and applied to a complete description of an academic model for inertial oceanic circulation, the Fofonoff flow.