Esmaili H, Mohammadzadeh H, Biderang M, Nattagh Najafi M. Thermodynamic geometry of a system with unified quantum statistics.
Phys Rev E 2024;
109:044104. [PMID:
38755881 DOI:
10.1103/physreve.109.044104]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2023] [Accepted: 02/23/2024] [Indexed: 05/18/2024]
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 (zZ^{*}) 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.
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