Statistical mechanics of quantum mechanical particles with hard cores

Abstract

The states of a quantum mechanical system of hard core particles are characterized as a convex weak *compact subset of the states over aC* algebra associated with the canonical (anti-) commutation relations. It is shown that the mean conditional entropy, i.e. entropy minus energy, can be defined as an affine upper semi-continuous function over theG-invariant hard core states whereG is an invariance group containing space translations. An abstract definition of the pressure and equilibrium states is given in terms of the maximum of the conditional entropy and it is shown that the pressureP _S obtained in this way satisfiesP≧P _S ≧P _∞ whereP andP _∞ are the thermodynamic pressures obtained from the usual Gibbs formalism with elastic wall, and repulsive wall, boundary conditions respectively. A number of additional results concerning the equilibrium states are also given.