Ideal Fermi gas in the Dunkl formalism

TL;DR

This paper explores how the Dunkl formalism alters the thermodynamic properties of an ideal Fermi gas, revealing the impact of deformation parameters on key physical quantities while maintaining Fermi-Dirac statistics.

Contribution

It introduces a novel application of the Dunkl formalism to Fermi gases, deriving modified thermodynamic expressions that incorporate reflection symmetric deformation effects.

Findings

Dunkl parameter affects internal energy and free energy.

Deformation influences entropy and heat capacity.

Altered properties impact compressibility and magnetic behavior.

Abstract

This paper investigates the thermodynamic properties of an ideal Fermi gas within the framework of the Dunkl formalism, which incorporates deformation effects through reflection symmetric differential operators. The formalism is applied to reformulate the creation and annihilation operators, leading to modified expressions for the fundamental thermodynamic quantities while preserving the underlying Fermi Dirac statistics. We derived modified expressions for the main thermodynamic quantities. In both the non degenerate and degenerate limits, we examined the effects of the Dunkl parameter on the internal energy, Helmholtz free energy, entropy, and heat capacity. Furthermore, we analyzed how the Dunkl deformation influences the isothermal compressibility, the average velocity of particles, and the Pauli paramagnetism.