Thermodynamic geometry for a non-extensive ideal gas

Highlights: • A generalized entropy relevant in non-equilibrium thermodynamics is used. • The thermodynamic curvature of the non-extensive ideal gas corresponding to the generalized entropy is calculated. • Effective interactions arise introduced by assuming a generalized statistics. • General features of superstatistics are confirmed using tools from Thermodynamic Geometry. • Results of the thermodynamic geometric analysis are compared with independent results of similar thermodynamic systems. - Abstract: A generalized entropy arising in the context of superstatistics is applied to an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric approach to thermodynamics. By means of the curvature/interaction hypothesis of the geometric approach to thermodynamic geometry it is found that as a consequence of considering a generalized statistics, an effective interaction arises but the interaction is not enough to generate a phase transition. This generalized entropy seems to be relevant in confinement or in systems with not so many degrees of freedom, so it could be interesting to use such entropies to characterize the thermodynamics of small systems.