New insight into the partition theory of integers related to problems of thermodynamics and mesoscopic physics

It is shown in the paper that the number p N ( M ) of partitions of a positive integer M into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic accuracy if one identifies M with energy and N with the number of particles. We use the Gentile statistics (a.k.a...

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Veröffentlicht in:Mathematical Notes 2017-07, Vol.102 (1-2), p.232-249
1. Verfasser: Maslov, V. P.
Format: Artikel
Sprache:eng
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Zusammenfassung:It is shown in the paper that the number p N ( M ) of partitions of a positive integer M into N positive integer summands coincides with the Bose and Fermi distributions with logarithmic accuracy if one identifies M with energy and N with the number of particles. We use the Gentile statistics (a.k.a. parastatistics) to derive self-consistent algebraic equations that enable one to construct the curves representing the least upper bound and the greatest lower bound of the repeated limits as M → ∞ and N → ∞. The resulting curves allow one to generalize the notion of BKT (Berezinskii–Kosterlitz–Thouless) topological phase transition and explaining a number of phenomena in thermodynamics and mesoscopic physics.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434617070252