Foundation of Statistical Mechanics, Statistical Ensembles

The thermodynamic limit in statistical thermodynamics of many-particle systems is an important but often overlooked issue in the various applied studies of condensed matter physics. To settle this issue, we review tersely the past and present disposition of thermodynamic limiting procedure in the structure of the contemporary statistical mechanics and our current understanding of this problem. We pick out the ingenious approach by Bogoliubov, who developed a general formalism for establishing the limiting distribution functions in the form of formal series in powers of the density. In that study, he outlined the method of justification of the thermodynamic limit when he derived the generalized Boltzmann equations. To enrich and to weave our discussion, we take this opportunity to give a brief survey of the closely related problems, such as the equipartition of energy and the equivalence and nonequivalence of statistical ensembles. The validity of the equipartition of energy permits one to decide what are the boundaries of applicability of statistical mechanics. The major aim of this work is to provide a better qualitative understanding of the physical significance of the thermodynamic limit in modern statistical physics of the infinite and "small" many-particle systems.

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REPRESENTATIVE ENSEMBLES IN STATISTICAL MECHANICS

International Journal of Modern Physics B ◽

10.1142/s0217979207035893 ◽

2007 ◽

Vol 21 (01) ◽

pp. 69-86 ◽

Cited By ~ 18

Author(s):

V. I. YUKALOV

Keyword(s):

Statistical Mechanics ◽

Condensed System ◽

Statistical Ensembles ◽

Self Consistent ◽

Statistical Systems ◽

Consistent Treatment

The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an illustration, a Bose-condensed system is considered. It is shown that a self-consistent treatment of the latter, using a representative ensemble, always yields a conserving and gapless theory.

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