We derive the thermodynamic curvature of a two dimensional ideal anyon gas of particles obeying fractional statistics. The statistical interactions of anyon gas can be attractive or repulsive. For attractive statistical interactions, thermodynamic curvature is positive and for repulsive statistical interactions, it is negative, which indicates a more stable anyon gas. There is a special case between the two where the thermodynamic curvature is zero. Small deviations from the classical limit will also be explored. PACS number(s): 05.20.-y, 67.10.Fj

We construct the thermodynamic geometry of an ideal q-deformed boson and fermion gas. We investigate some thermodynamic properties such as the stability and statistical interaction. It will be shown that the statistical interaction of qdeformed boson gas is attractive, while it is repulsive for the q-deformed fermion one. Also, we will consider the singular point of the thermodynamic curvature to obtain some new results about the condensation of q-deformed bosons and show that there exist a finite critical phase transition temperature even in low dimensions. It is shown that the thermodynamic curvature of q-deformed boson and fermion quantum gases diverges as a power-law function with respect to temperature at zero temperature limit.PACS number(s): 05.70.Fh

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. PACS number(s): 67.10.Fj

Following our earlier work on the Ruppeiner geometry of an anyon gas [B. Mirza and H. Mohammadzadeh, Phys. Rev. E 78, 021127 (2008)], we will derive nonperturbative thermodynamic curvature of a two-dimensional ideal anyon gas. At different values of the thermodynamic parameter space, some unique and interesting behaviors of the anyon gas are explored. A complete picture of attractive and repulsive phases of the anyon gas is given.

In some models, dark matter is considered as a condensate bosonic system. In this paper, we prove that condensation is also possible for particles that obey infinite statistics and derive the critical condensation temperature. We argue that a condensed state of a gas of very weakly interacting particles obeying infinite statistics could be considered as a consistent model of dark matter.