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

@article{Ellis2000LargeDP, title={Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles}, author={Richard S. Ellis and Kyle Haven and Bruce Turkington}, journal={Journal of Statistical Physics}, year={2000}, volume={101}, pages={999-1064} }

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…

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