Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles

Preprint

11 December 2000

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0012081

Abstract

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles.

Keywords

EQUIVALENCE AND NONEQUIVALENCE
LARGE DEVIATION PRINCIPLES
NONEQUIVALENCE RESULTS
COMPLETE EQUIVALENCE
TURBULENCE
ENSEMBLE
MODELS

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