Issue
EPL
Volume 84, Number 3, November 2008
Article Number 30006
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/84/30006
Published online 30 October 2008
EPL, 84 (2008) 30006
DOI: 10.1209/0295-5075/84/30006

Classical typicality of the canonical distribution

A. R. Plastino1, 2, 3 and A. Daffertshofer4

1   Instituto Carlos I de Física Teórica y Computacional, University of Granada - Granada, Spain, EU
2   National University La Plata, CREG-UNLP-CONICET - C.C. 727, 1900 La Plata, Argentina
3   Physics Department, University of Pretoria - Pretoria 0002, South Africa
4   Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam van der Boechorststraat 9, 1081 BT, Amsterdam, The Netherlands, EU

arplastino@maple.up.ac.za
marlow@fbw.vu.nl

received 9 July 2008; accepted in final form 24 September 2008; published November 2008
published online 30 October 2008

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.

PACS
05.20.Gg - Classical ensemble theory.

© EPLA 2008