States of Classical Statistical Mechanics

Abstract

A state of an infinite system in classical statistical mechanics is usually described by its correlation functions. We discuss here other descriptions in particular: as (1) a state on a B* algebra; (2) a collection of density distributions; (3) a field theory; (4) a measure on a ``space of configurations of infinitely many particles.'' We consider the relations between these various descriptions and prove, under very general conditions, an integral representation of a state as superposition of ``extremal invariant states'' corresponding to pure thermodynamical phases.