Nonuniqueness of Canonical Ensemble Theory arising from Microcanonical Basis

Abstract

Given physical systems, counting rule for their statistical mechanical descriptions need not be unique, in general. It is shown that this nonuniqueness leads to the existence of various canonical ensemble theories which equally arise from the definite microcanonical basis. Thus, the Gibbs theorem for canonical ensemble theory is not universal, and the maximum entropy principle is to be appropriately modefied for each physical context.Comment: 13 pages; This is a thoroughly revised version of the original preprint which has now appearted in print. It also corrects several errors and misstatements in the published version. The main conclusions of the paper however remain intac