Ensemble Dependence of Fluctuations: Canonical Microcanonical Equivalence of Ensembles

• DOI: 10.1007/s10955-017-1830-y
• Publication Date: 2017-06-29T04:24:55Z
• Authors: Nicoletta Cancrini; Stefano Olla
• Keywords: Microcanonical ensemble; Thermodynamic limit; Grand canonical ensemble; Statistical ensemble; Central limit theorem

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.