New insight into the partition theory of integers related to problems of thermodynamics and mesoscopic physicsстатья
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Аннотация: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 -> a and N -> a. 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.