Thermodynamics of Classical Systems on Noncommutative Phase Space

TL;DR

This paper develops a statistical mechanics framework on noncommutative phase space, extending classical thermodynamics to systems with noncommuting variables, and applies it to key physical models.

Contribution

It introduces a canonical ensemble theory for noncommutative phase space and demonstrates its application to classical models like ideal gases and harmonic oscillators.

Findings

Formulated a statistical mechanics approach on noncommutative phase space

Applied the theory to ideal gas, relativistic gas, and harmonic oscillator

Provided insights into thermodynamics in noncommutative settings

Abstract

We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas, and the 3-dimensional harmonic oscillator.