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 language | English |
---|---|
Article number | 30006 |
Journal | Europhysics Letters |
Volume | 84 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Nov 2008 |