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Matematicheskie Zametki, 2017, Volume 102, Issue 2, paper published in the English version journal
(Mi mzm11760)
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This article is cited in 8 scientific papers (total in 8 papers)
Papers published in the English version of the journal
New Insight into the Partition Theory of Integers
Related to Problems of Thermodynamics
and Mesoscopic Physics
V. P. Maslovab a National Research University Higher School of Economics,
Moscow, Russia
b Ishlinsky Institute for Problems in Mechanics, Moscow, Russia
Abstract:
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 $M\to \infty$ and
$N\to \infty$. 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.
Keywords:
tropical analysis, logarithmic accuracy, turbulence,
enveloping series, topological phase transition, boson, fermion,
critical energy, mesoscopic physics, Erdős formula,
Hardy–Ramanujan theorems, liquid-drop model of nucleus, neutron, A-bomb.
Received: 11.03.2017
Citation:
V. P. Maslov, “New Insight into the Partition Theory of Integers
Related to Problems of Thermodynamics
and Mesoscopic Physics”, Math. Notes, 102:2 (2017), 232–249
Linking options:
https://www.mathnet.ru/eng/mzm11760
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