Thermodynamic geometry of a system with unified quantum statistics.

Abstract

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 δ. An intrinsic statistical interaction becomes attractive for δ≤0.5, maintaining positive thermodynamic curvature across the entire physical range. In the range 0.5<δ<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^{*}) at which the thermodynamic curvature changes sign. Below (z<Z^{*}) and above (z>Z^{*}) this critical point, the statistical behavior mimics fermions and bosons, respectively. We explore the system's statistical behavior for various δ 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 δ values in various dimensions.