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

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

2000-12-11

arxiv.org/abs/math/0012081v1

Mathematics

Probability

57 pages

Scientific paper

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.

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