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New Insight into the Partition Theory of Integers Related to Problems of Thermodynamics and Mesoscopic Physics
Mathematical notes. 2017. Vol. 102. No. 2. P. 234–251.
It is shown in the paper that the number pN(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.
Priority areas:
mathematics
Language:
English
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Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
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The shape of the heliosphere, regarded as comet-like since the 1960s, has recently been the subject of intense debate in the last decade. There is disagreement as to whether the heliospheric tail extends to ∼10,000 au in a comet-like shape or if it is short (∼400 au) with a split. Energetic neutral atom (ENA) maps from ...
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Overheating remains a critical limitation in high-performance electronic and computing systems,
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Fortuna A. S., A.I. Kartsev, Gorshenkov M. V. et al., Journal of Alloys and Compounds 2026 Vol. 1070 Article 188711
The τ-phase in Mn-Al-Ga alloys is a promising candidate for rare-earth-free permanent magnets. This study re-veals that the τ(γ₂)-phase in rapidly quenched Mn55Al36Ga9 ribbons contains a high density of dislocations, which
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Dikhtievskaya K., Argunov E., Карцев А. И. et al., The Journal of Physical Chemistry Letters 2026 Vol. 17 No. 17 P. 4999–5004
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Duran E. ., Pulgar A., Izquierdo R. et al., Physica Status Solidi (A) Applications and Materials 2026 Vol. 223 No. 7 Article e202500942
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Borisov V., Danilov V., Электросвязь 2025 № 12 С. 73–84
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Elesin L., Shilov A., Jana S. et al., Advanced Functional Materials 2026 P. 1–10
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Medvedev V., / Series arXiv "math". 2026.
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Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
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