Nonuniqueness of canonical ensemble theory arising from microcanonical basis

Given a physical system, counting rule fur its statistical mechanical descr iption need nut be unique, in general. It is shown that this nonuniqueness leads to the existence of various canonical ensemble theories, which equall y arise from the definite microcanonical basis. Thus, the Gibbs theorem for canonical ensemble theory is not universal, and maximum entropy principle is to be appropriately modified for each physical context. (C) 2000 Publish ed by Elsevier Science B.V. PACS: 05.20.-y; 05.20.Gg; 05.45.Df; 05.90. + m.