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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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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DOI: https://doi.org/10.1007/BF01199021
Mathematics Subject Classification (1991)
- 60F10
- 60G55
- 60K35
- 82B05
- 82B21