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Statistical mechanics in the extended Gaussian ensemble
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The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 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 ß and ¿ which allow one 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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JOHAL, Ramandeep S., PLANES VILA, Antoni and VIVES I SANTA-EULÀLIA, Eduard. Statistical mechanics in the extended Gaussian ensemble. Physical Review E. 2003. Vol. 67, num. 5, pags. 056113-1-056113-8. ISSN 1539-3755. [consulted: 24 of August of 2026]. Available at: https://hdl.handle.net/2445/18741