# Perturbative Thermodynamic Geometry of Nonextensive Ideal Classical, Bose and Fermi Gases

## TL;DR

This paper explores how nonextensive statistical mechanics alters the thermodynamic geometry of ideal classical, Bose, and Fermi gases, revealing changes in interaction nature and phase behavior due to the nonextensive parameter.

## Contribution

It provides a perturbative analysis of thermodynamic geometry in nonextensive gases, identifying how nonextensivity affects statistical interactions and phase transitions.

## Key findings

- Nonextensive Bose (Fermi) gases exhibit attractive (repulsive) interactions similar to extensive cases.
- The thermodynamic curvature's value is modified by the nonextensive parameter.
- A critical fugacity $z^{*}$ marks a change in the sign of thermodynamic curvature, indicating different interaction regimes.

## Abstract

We investigate perturbative thermodynamic geometry of nonextensive ideal Classical, Bose and Fermi gases.We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, $z^{*}$, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for $z<z^{*}$ ($z>z^{*}$) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.