Statistical mechanics of free particles on space with Lie type noncommutativity

TL;DR

This paper explores how Lie type noncommutativity influences the thermodynamics of free particles, providing new definitions for finite volume and analyzing various limits, including specific cases like SU(2) and SO(3).

Contribution

It introduces a framework for thermodynamics on noncommutative spaces with Lie algebra structures, including finite volume definitions and partition function calculations.

Findings

Thermodynamic properties are derived from the partition function.

Different pressure definitions are shown to coincide when noncommutativity vanishes.

Explicit partition functions are calculated for SU(2) and SO(3) groups.

Abstract

Effects of Lie type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.