The exclusion principle and the evolution of matter in statistics of particles with hierarchical structure

M.Yu. Romanovsky^†^a, b, c
^aANO National Center for Physics and Mathematics, Parkovaya Str. 1, build. 3, Sarov, Nizhny Novgorod Region, 607182, Russian Federation
^bRussian National Research Medical University named after N.I. Pirogov, Ostrovitianov str. 1, Moscow, 117997, Russian Federation
^cPI "Science and Innovation", Bol'shaya Ordynka str. 24, Moscow, 119017, Russian Federation

Statistics of the most probable energy distributions are constructed and investigated in systems with many particles, some of which are contained (or delimited) within other particles, as well as in systems with particles delimited within other particles, which, in turn, are delimited within third particles. The statistics of the distributions of such particles with respect to the maximum and minimum energy values turn out to coincide with those obtained in the initial combinatorial solution. The results provide a basis for proving the Pauli exclusion principle, the minimality of energy release in various processes, and the absence of particles with negative energy, as well as describe the complication of the structure of matter.

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Keywords: most probable distributions, distributions of extremes, hierarchical structures, delimitation, Pauli exclusion principle, matter complication
PACS: 02.50.−r, 05.20.−y, 12.40.Ee, 31.15.bt (all)
DOI: 10.3367/UFNe.2025.05.040010
URL: https://ufn.ru/en/articles/2026/7/e/
Citation: Romanovsky M Yu "The exclusion principle and the evolution of matter in statistics of particles with hierarchical structure" Phys. Usp. 69 (7) (2026)

Received: 28th, July 2025, accepted: 21st, May 2025

Оригинал: Романовский М Ю «Принцип запрета и эволюция вещества в статистиках частиц с иерархической структурой» УФН 196 763–778 (2026); DOI: 10.3367/UFNr.2025.05.040010

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