Thermodynamic geometry of a system with unified quantum statistics

We investigate the thermodynamic characteristics of unified quantum statistics, a framework exhibiting a crossover between Bose-Einstein and Fermi-Dirac statistics by varying a generalization parameter delta. An intrinsic statistical interaction becomes attractive for delta <= 0.5, maintaining positive thermodynamic curvature across the entire physical range. In the range 0.5 < delta < 1, the system predominantly displays Fermi-like behavior at high temperatures. Conversely, at low temperatures, the thermodynamic curvature is positive, resembling bosonic behavior. Further temperature reduction induces a transition into the condensate phase. We introduce a critical fugacity (z = Z(& lowast;)) at which the thermodynamic curvature changes sign. Below (z < Z(& lowast;)) and above (z >Z(& lowast;)) this critical point, the statistical behavior mimics fermions and bosons, respectively. We explore the system's statistical behavior for various delta values with respect to temperature, determining the critical fugacity and temperature-dependent condensation. Finally, we analyze specific heat as a function of temperature and condensation phase transition temperature for different delta values in various dimensions.