Microscopic and macroscopic properties of A-superstatistics

TL;DR

This paper explores the microscopic and macroscopic properties of A-superstatistics related to the Lie superalgebra sl(1|n), including its algebraic structure, Fock spaces, Pauli principle, and thermal properties, with explicit formulas for the grand partition function.

Contribution

It provides a detailed analysis of A-superstatistics, introducing its algebraic framework, Fock space structure, and thermal behavior, with explicit formulas for key statistical quantities.

Findings

Explicit grand partition function derived for A-superstatistics.

Formulation of the Pauli principle for this superstatistics.

Analysis of thermal properties under specific energy configurations.

Abstract

The microscopic and the macroscopic properties of A-superstatistics, related to the class A(0,n-1)\equiv sl(1|n) of simple Lie superalgebras are investigated. The algebra sl(1|n) is described in terms of generators f_1^\pm, >..., f_n^\pm, which satisfy certain triple relations and are called Jacobson generators. The Fock spaces of A-superstatistics are investigated and the Pauli principle of the corresponding statistics is formulated. Some thermal properties of A-superstatistics are constructed under the assumption that the particles interact only via statistical interaction imposed by the Pauli principle. The grand partition function and the average number of particles are written down explicitly in the general case and in two particular examples: 1) the particles have one and the same energy and chemical potential; 2) the energy spectrum of the orbitals is equidistant.