On the extension of invariant partial states in statistical mechanics

Abstract

We consider a class of physical systems often encountered in such theories as statistical mechanics, namely those which admit an amenable group as a group of symmetries. We first establish the existence of invariant state(s) with respect to the symmetry group considered. We next introduce the notion of (extremal) potentially invariant states for an reduced description of the physical system considered; we then show that every such state can be extened to an (extremal) invariant state corresponding to a complete description.