Thermodynamic geometry of fractional statistics

We extend our earlier study about the fractional exclusion statistics to higher dimensions in full physical range and in the nonrelativistic and ultrarelativistic 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 nonpure bosonic system which is similar to the Bose-Einstein condensation and the phase transition temperature will be worked out.