Ensemble Dependence of Fluctuations: Canonical Microcanonical Equivalence of Ensembles
Cancrini, Nicoletta; Olla, Stefano (2017), Ensemble Dependence of Fluctuations: Canonical Microcanonical Equivalence of Ensembles, Journal of Statistical Physics, 168, 4, p. 707 - 730. 10.1007/s10955-017-1830-y
TypeArticle accepté pour publication ou publié
Journal nameJournal of Statistical Physics
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Abstract (EN)We study the equivalence of microcanonical and canonical ensembles in continuous systems, in the sense of the convergence of the corresponding Gibbs measures and the first order corrections. We are particularly interested in extensive observables, like the total kinetic energy. This result is obtained by proving an Edgeworth expansion for the local central limit theorem for the energy in the canonical measure, and a corresponding local large deviations expansion. As an application we prove a formula due to Lebowitz-Percus-Verlet that express the asymptotic microcanonical variance of the kinetic energy in terms of the heat capacity.
Subjects / Keywordsmicro-canonical ensemble; equivalence of ensembles; local central limit theorems; local large deviations
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