LARGE DEVIATIONS AND THE EQUIVALENCE OF ENSEMBLES FOR GIBBSIAN PARTICLE-SYSTEMS WITH SUPERSTABLE INTERACTION

For Gibbsian systems of particles in R(d), we investigate large deviat ions of the translation invariant empirical fields in increasing boxes . The particle interaction is given by a superstable, regular pair pot ential. The large deviation principle is established for systems with free or periodic boundary conditions and, under a stronger stability h ypothesis on the potential, for systems with tempered boundary conditi ons, and for tempered (infinite-volume) Gibbs measures. As a by-produc t we obtain the Gibbs variational formula for the pressure. We also pr ove the asymptotic equivalence of microcanonical and grand canonical G ibbs distributions and establish a variational expression for the ther modynamic entropy density.