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 |
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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. |
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ISSN: | 0001-4346 1067-9073 1573-8876 |
DOI: | 10.1134/S0001434617070252 |