Hans-Otto Georgii
Large deviations and the equivalence of ensembles for Gibbsian particle
systems with superstable interaction
(66K, latex3)

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.