Thermodynamic geometry, transition between attractive and repulsive interactions and condensation of dual statistics

We consider new generalized statistics based on the generalization of statistical weight. We work out the thermodynamic curvature of an ideal gas with particles obeying such generalized statistics. For different values of generalization parameters; p and q, we observe that both attractive and repulsive intrinsic statistical interaction is expected. As long as p ⩾ q, the thermodynamic curvature is positive in full physical range. We show that for p < q, generally dominant behavior in high temperature is Fermi-like while in low temperature, the thermodynamic curvature is positive and the systems behaves such as bosons. Also, by more decreasing of the temperature, the system transits to the condensate phase. In fact, the attractive statistical interaction is related to parameter p, while by increasing the value of q, the repulsive interaction is induced. Explicitly, the specified fugacity ($z=z_{p,q}^{\ast }$) of the system, where the sign of thermodynamic curvature is changed and for $z<z_{p,q}^{\ast }$ (z > z∗_p,q) the statistical behavior is fermion like (boson like ), is explored. Also, we extract the variation of statistical behavior of the system for different values of generalization parameters with respect to the temperature. Finally, we investigate the condensation phase transition temperature of the system for different values of generalization parameters. (paper)