Physical Sciences and Mathematics Commons^™

Nonequivalent Statistical Equilibrium Ensembles And Refined Stability Theorems For Most Probable Flows, Richard S. Ellis, Kyle Haven, Bruce Turkington

Richard S. Ellis

Statistical equilibrium models of coherent structures in two-dimensional and barotropic quasi-geostrophic turbulence are formulated using canonical and microcanonical ensembles, and the equivalence or nonequivalence of ensembles is investigated for these models. The main results show that models in which the energy and circulation invariants are treated microcanonically give richer families of equilibria than models in which they are treated canonically. For each model, a variational principle that characterizes its equilibrium states is derived by large deviation techniques. An analysis of the two different variational principles resulting from the canonical and microcanonical ensembles reveals that their equilibrium states coincide if and …