Ensemble dependence of fluctuations and the canonical/micro-canonical equivalence of ensembles

Abstract

We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures. This is obtained by proving a local central limit theorem and a local large deviations principle. As an application we prove a formula due to Lebowitz-Percus-Verlet. It gives mean square fluctuations of an extensive observable, like the kinetic energy, in a classical micro canonical ensemble at fixed energy.

Cited by in corpus (5)

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• Decay of correlations and uniqueness of the infinite-volume Gibbs measure of the canonical ensemble of 1d-lattice systems
• Modified Jarzynski equality in a microcanonical ensemble
• Local moderate and precise large deviations via cluster expansions
• Equivalence of the grand canonical ensemble and the canonical ensemble on 1d-lattice systems