Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction
type: Item
instance of: scholarly article
title: Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction
zbMATH Open document ID: 0803.60097
DOI: 10.1007/BF01199021
author: Hans-Otto Georgii
publication date: 1994-10-13T00:00:00Z
review text: For Gibbsian systems of particles in \(\mathbb{R}^ d\), we investigate large deviations of the translation invariant empirical fields in increasing boxes. The particle interaction is given by a superstable, regular pair potential. The large deviation principle is established for systems with free or periodic boundary conditions and, under a stronger stability hypothesis on the potential, for systems with tempered boundary conditions, and for tempered (infinite-volume) Gibbs measures. As a by- product we obtain the Gibbs variational formula for the pressure. We also prove the asymptotic equivalence of microcanonical and grand canonical Gibbs distributions and establish a variational expression for the thermodynamic entropy density.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 82B21
zbMATH DE Number: 639355
zbMATH Keywords: Gibbsian systems of particles
zbMATH Keywords: translation invariant empirical fields
zbMATH Keywords: microcanonical
zbMATH Keywords: grand canonical
zbMATH Keywords: thermodynamic entropy density
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01199021
OpenAlex ID: W1983078392
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 639355