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Entropy 2016, 18(7), 259; doi:10.3390/e18070259

Ensemble Equivalence for Distinguishable Particles

Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC), Consejo Superior de Investigaciones Científicas (CSIC)–Universitat de les Illes Balears (UIB), Palma de Mallorca 07122, Spain
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Academic Editor: Antonio M. Scarfone
Received: 29 April 2016 / Revised: 5 July 2016 / Accepted: 8 July 2016 / Published: 13 July 2016
(This article belongs to the Section Statistical Mechanics)
View Full-Text   |   Download PDF [255 KB, uploaded 13 July 2016]

Abstract

Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. In this paper, we present evidence that a commonly used expression for the partition function of a system of distinguishable particles leads to huge fluctuations of the number of particles in the grand canonical ensemble and, consequently, to nonequivalence of statistical ensembles. We will show that the alternative definition of the partition function including, naturally, Boltzmann’s correct counting factor for distinguishable particles solves the problem and restores ensemble equivalence. Finally, we also show that this choice for the partition function does not produce any inconsistency for a system of distinguishable localized particles, where the monoparticular partition function is not extensive. View Full-Text
Keywords: entropy; distinguishable particles; ensemble equivalence entropy; distinguishable particles; ensemble equivalence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Fernández-Peralta, A.; Toral, R. Ensemble Equivalence for Distinguishable Particles. Entropy 2016, 18, 259.

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