Statistical Mechanics in the Extended Gaussian Ensemble

Details Statistical Mechanics in the Extended Gaussian Ensemble Statistical Mechanics in the Extended Gaussian Ensemble

2003-07-25

arxiv.org/abs/cond-mat/0307646v1

Physics

Condensed Matter

Statistical Mechanics

Revtex 4, 8 pages, 8 figures

Scientific paper

10.1103/PhysRevE.68.056113

The extended gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. The new ensemble is a further extension of the Gaussian ensemble introduced by J. H. Hetherington [J. Low Temp. Phys. {\bf 66}, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the Maximum Statistical Entropy Principle. The probability of each microstate depends on two parameters $\beta$ and $\gamma$ which allow to fix, independently, the mean energy of the system and the energy fluctuations respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the $q$-exponential distribution. As an example, an application to a system with few independent spins is presented.

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