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Matematicheskie Zametki, 2017, Volume 102, Issue 2, paper published in the English version journal (Mi mzm11760)  

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
Citations (8)
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
English version:
Mathematical Notes, 2017, Volume 102, Issue 2, Pages 232–249
DOI: https://doi.org/10.1134/S0001434617070252
Bibliographic databases:
Document Type: Article
Language: English
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
Citation in format AMSBIB
\Bibitem{Mas17}
\by V.~P.~Maslov
\paper New Insight into the Partition Theory of Integers
Related to Problems of Thermodynamics
and Mesoscopic Physics
\jour Math. Notes
\yr 2017
\vol 102
\issue 2
\pages 232--249
\mathnet{http://mi.mathnet.ru/mzm11760}
\crossref{https://doi.org/10.1134/S0001434617070252}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000413842800025}
\elib{https://elibrary.ru/item.asp?id=29485874}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029002741}
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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