Probability distribution of (Schw\"{a}mmle and Tsallis) two-parameter entropies and the Lambert W-function

Abstract

We investigate a two-parameter entropy introduced by Schw\"{a}mmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert W-function which has been used in many branches of physics, especially in fractal structures. Also, extensivity of $S_{q,q'}$ is discussed and a relationship is found to exist between the probabilities of a composite system and its subsystems so that the two-parameter entropy, $S_{q,q'}$, is extensive.