Classical typicality of the canonical distribution

A.R. Plastino, A. Daffertshofer

    Research output: Contribution to JournalArticleAcademicpeer-review

    Abstract

    We consider the typicality of the canonical ensemble's probability distribution from a classical perspective, resuming recent discussions on quantum-mechanical aspects of canonical typicality. In the conventional derivation of the classical canonical distribution for a system S that is weakly coupled to a heat bath B, it is assumed that the composite S+B is represented by the microcanonical ensemble i.e., by a uniform probability distribution on an energy shell of the composite S+B. Here we show that for a very large heat bath almost all probability distributions defined on this energy shell behave according to the microcanonical ensemble, yielding a marginal probability distribution for S of the canonical form. Consequently, the classical canonical distribution can be regarded as much more "typical" than suggested by the standard derivation.

    Original languageEnglish
    Article number30006
    JournalEurophysics Letters
    Volume84
    Issue number3
    DOIs
    Publication statusPublished - 1 Nov 2008

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