Thermodynamic Geometry of Fractional Statistics

Abstract

We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the non-relativistic and ultra-relativistic limits. Also, two other fractional statistics, namely Gentile and Polychronakos fractional statistics, will be considered and similarities and differences between these statistics will be explored. Thermodynamic geometry suggests that a two dimensional Haldane fractional exclusion gas is more stable than higher dimensional gases. Also, a complete picture of attractive and repulsive statistical interaction of fractional statistics is given. For a special kind of fractional statistics, by considering the singular points of thermodynamic curvature, we find a condensation for a non-pure bosonic system which is similar to the Bose-Einstein condensation and the phase transition temperature will be worked out.

29 pages, 12 figures

References in corpus (8)

• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Unified geometric description of black hole thermodynamics
• Ruppeiner Geometry of Anyon Gas
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Nonperturbative Thermodynamic Geometry of Anyon Gas
• Thermodynamics of ideal quantum gas with fractional statistics in D dimensions
• Statistics of Anyon Gas and the Factorizable Property of Thermodynamic Quantities
• Comment on ``Quantum Statistical Mechanics of an Ideal Gas with Fractional Exclusion Statistics in Arbitrary Dimension"