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29 March 2024
 
  » arxiv » math.PR/0012081

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Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles
R. S. Ellis ; K. Haven ; B. Turkington ;
Date 11 Dec 2000
Subject Probability; Mathematical Physics; Optimization and Control MSC-class: 60F10;82B10 | math.PR math-ph math.MP math.OC
AbstractWe 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.
Source arXiv, math.PR/0012081
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