On the inequivalence of statistical ensembles

Details On the inequivalence of statistical ensembles On the inequivalence of statistical ensembles

2001-12-12

arxiv.org/abs/cond-mat/0112222v2

Phys.Rev. E 66 (2002) 046108

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.66.046108

We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.

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