Thermodynamic geometry, condensation and Debye model of two-parameter deformed statistics

Abstract

We consider the statistical distribution function of a two parameter deformed system, namely qp-deformed bosons and fermions. Using a thermodynamic geometry approach, we derive the thermodynamic curvature of an ideal gas with particles obeying qp-bosons and qp-fermions. We show that the intrinsic statistic interaction of qp-bosons is attractive in all physical ranges, while it is repulsive for qp-fermions. Also, the thermodynamic curvature of qp-boson gas is singular at a specified value of fugacity and therefore, a phase transition such as Bose–Einstein condensation can take place. In the following, we compare the experimental and theoretical results of temperature-dependent specific heat capacity of some metallic materials in the framework of q and qp-deformed algebras.