Fractional exclusion statistics of two-species gases

The thermodynamics of two-species gases described by the Haldane exclusion statistics is investigated. I use the high-temperature perturbation to find the third Virial coefficient for the gas in an arbitrary dimension. The perturbative result indicates that the two-dimensional thermodynamic potential becomes the linear function of the element of the Haldane statistics matrix, if the matrix is symmetric and particle mass is species independent. I also present a nonperturbative method to prove this factorizable property and an exact expression of the thermodynamic potential is suggested.