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Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction
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  • Published: June 1994

Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction

  • Hans-Otto Georgii1 

Probability Theory and Related Fields volume 99, pages 171–195 (1994)Cite this article

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  • 41 Citations

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Summary

For Gibbsian systems of particles inR 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.

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Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstrasse 39, D-80333, München, Germany

    Hans-Otto Georgii

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  1. Hans-Otto Georgii
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Georgii, HO. Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction. Probab. Th. Rel. Fields 99, 171–195 (1994). https://doi.org/10.1007/BF01199021

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  • Received: 02 June 1993

  • Revised: 03 January 1994

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01199021

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Mathematics Subject Classification (1991)

  • 60F10
  • 60G55
  • 60K35
  • 82B05
  • 82B21
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