Macroscopic properties of A-statistics

TL;DR

This paper explores the thermodynamic properties of A-statistics, a quantum statistical framework based on the Lie algebra sl(n+1), analyzing specific cases and deriving explicit formulas for key thermodynamic quantities.

Contribution

It provides a detailed investigation of the thermal properties of A-statistics, including explicit calculations of grand partition functions and particle numbers for particular scenarios.

Findings

Derived explicit grand partition functions for A-statistics.

Analyzed three specific cases with different energy and chemical potential configurations.

Provided formulas for average particle numbers in A-statistics systems.

Abstract

A-statistics is defined in the context of the Lie algebra sl(n+1). Some thermal properties of A-statistics are investigated under the assumption that the particles interact only via statistical interaction imposed by the Pauli principle of A-statistics. Apart from the general case, three particular examples are studied in more detail: (a) the particles have one and the same energy and chemical potential; (b) equidistant energy spectrum; (c) two species of particles with one and the same energy and chemical potential within each class. The grand partition functions and the average number of particles are among the thermodynamical quantities written down explicitly.