Thermodynamic Geometry of Deformed Bosons and Fermions

TL;DR

This paper develops the thermodynamic geometry for q-deformed boson and fermion gases, revealing their stability, statistical interactions, and phase transition behaviors, including a finite critical temperature in low dimensions.

Contribution

It introduces a thermodynamic geometric framework for q-deformed quantum gases and uncovers new insights into their phase transitions and interaction properties.

Findings

Q-deformed boson gas exhibits attractive statistical interaction.

Q-deformed fermion gas exhibits repulsive statistical interaction.

Finite critical phase transition temperature exists in low dimensions.

Abstract

We construct the thermodynamic geometry of an ideal q-deformed boson and fermion gas. We investigate some thermodynamic properties such as the stability and statistical interaction. It will be shown that the statistical interaction of q-deformed boson gas is attractive, while it is repulsive for the q-deformed fermion one. Also, we will consider the singular point of the thermodynamic curvature to obtain some new results about the condensation of q-deformed bosons and show that there exist a finite critical phase transition temperature even in low dimensions. It is shown that the thermodynamic curvature of q-deformed boson and fermion quantum gases diverges as a power-law function with respect to temperature at zero temperature limit.