Partial equivalence of statistical ensembles and kinetic energy

Lapo Casetti and Michael Kastner

Physica A: Statistical Mechanics and its Applications, 2007, vol. 384, issue 2, 318-334

Abstract: The phenomenon of partial equivalence of statistical ensembles is illustrated by discussing two examples, the mean-field XY and the mean-field spherical model. The configurational parts of these systems exhibit partial equivalence of the microcanonical and the canonical ensemble. Furthermore, the configurational microcanonical entropy is a smooth function, whereas a nonanalytic point of the configurational free energy indicates the presence of a phase transition in the canonical ensemble. In the presence of a standard kinetic energy contribution, partial equivalence is removed and a nonanalyticity arises also microcanonically. Hence in contrast to the common belief, kinetic energy, even though a quadratic form in the momenta, has a nontrivial effect on the thermodynamic behaviour. As a by-product we present the microcanonical solution of the mean-field spherical model with kinetic energy for finite and infinite system sizes.

Keywords: Ensembles (non)equivalence and partial equivalence; Kinetic energy; Phase transitions; Thermodynamic singularities (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:384:y:2007:i:2:p:318-334

DOI: 10.1016/j.physa.2007.05.043

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