93-180 Hans-Otto Georgii
Large deviations and the equivalence of ensembles for Gibbsian particle systems with superstable interaction (66K, latex3) Jun 16, 93
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Abstract. For Gibbsian systems of particles in $\R^d$, we investigate large deviations of the stationary 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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