Statistical Properties of Many-Particle Systems with Hierarchical Structure

Many-particle systems contained inside other particles (problem 1), as well as systems of particles delimited inside other particles, which, in turn, are delimited inside the third particles (problem 2), are considered. Under natural assumptions about conserved quantities such as the total number of all particles, the total energy, and a number of others, the most probable energy distributions of particles, true (internal) and external observables, are studied. The results of problems 1 and 2 can be interpreted as the separation of bottom level particles into kinds with different distributions observed in different experiments. In single-particle observations in the full probability problem 1, an effective Pauli principle arises in a consistent manner.