Radial distribution function within the third version of the Tsallis statistical mechanics

Nowadays, a variety of physical systems have been known whose thermodynamic behavior, due to non-extensive effects, is not explicable by the common Boltzmann-Gibbs (BG) statistical mechanics. Thus, the correction of the BG entropy seems to be essential. In this regard, an efficient extension has been promoted by Tsallis, which is based on a generalized entropic form. In this study, a new equation is derived for the Radial Distribution Function (RDF) by taking into account the third version of the Tsallis statistics. To this end, probability distribution function is applied within the third version of the Tsallis statistics. Moreover, a closed formula is proposed for RDF. The momenta and the coordinates are independent in this equation. The effect of the non-extensivity parameter, q, on the RDF of a Lennard-Jones fluid, was investigated. At low densities, the results of the numerical calculations performed for RDF indicated that, the correlation increases with an increase in the values of q. Increase of the non-extensivity parameter and that of  has similar effects.