Probability distribution of (Schwämmle and Tsallis) two-parameter entropies and the Lambert WW-function

We investigate a two-parameter entropy introduced by Schwämmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert WW-function which has been used in many branches of physics, especially in fractal structures. Also, extensivity of Sq,q′Sq,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, Sq,q′Sq,q′, is extensive.