Physical Sciences and Mathematics Commons^™

The Generalized Canonical Ensemble And Its Universal Equivalence With The Microcanonical Ensemble, M Costeniuc, Rs Ellis, H Touchette, B Turkington

Mathematics and Statistics Department Faculty Publication Series

This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a generalized canonical ensemble that satisfies a strong form of equivalence with the microcanonical ensemble that we call universal equivalence. The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. For example, if the microcanonical entropy is C², then universal equivalence of ensembles holds with g taken from a class …