A Statistical Analysis of Anharmonic Gases

TL;DR

This paper investigates the effects of anharmonic perturbations on gases of particles, analyzing both classical and quantum cases, and provides formulas for partition functions and average energies.

Contribution

It introduces a detailed analysis of anharmonic gases, including relativistic effects, and derives key thermodynamic quantities for these systems.

Findings

Partition function expressions derived for anharmonic gases

Average energy formulas obtained for classical and quantum cases

Relativistic effects incorporated into the analysis

Abstract

In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles. In the first case, the partition function is computed and stated. In both cases, expressions for the average energy are obtained.