Most probable distributions and distributions of extremes for particle systems with hierarchical structures

Abstract

The problem of the most probable distributions on energy is studied in a combinatorial formulation, under the natural hypotheses regarding conservation laws, such as conservation of the total number of particles, total energy, etc. The particle distributions on the maximum and minimum energies are obtained and coincide with those found in the framework of the original combinatorial treatment. Two types of energy distributions for delimited particles are obtained. The results can be interpreted as sorting of particles based on their statistical mechanics behavior observed in various experiments. An effective Pauli principle arises in a non-contradictory way in one-particle observations both for once- and twice-delimited systems in the combinatorial formulation as well as in the problem of distributions on maximum and minimum energies. Many of the distributions obtained describe particles that do not have negative energy states.