Thermodynamic fermion-boson symmetry in harmonic oscillator potentials

TL;DR

This paper uncovers a unique thermodynamic symmetry between fermionic and bosonic quantum gases in harmonic oscillator potentials, linking their partition functions through negative temperatures.

Contribution

It reveals a novel fermion-boson symmetry in ideal quantum gases within harmonic oscillator potentials, connecting their thermodynamics via negative temperature extensions.

Findings

Bosonic and fermionic partition functions are related through negative temperatures.

The symmetry applies specifically to odd-dimensional harmonic oscillator potentials.

This connection provides new insights into quantum statistical mechanics.

Abstract

A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to negative temperatures, and vice versa.