q-generalization of quantum phase-space representations

We generate a family of phase space, thermal coherent-state's representations, within the framework of Tsallis' Generalized Statistical Mechanics and study their properties. Our protagonists are q-gaussian distributions. We obtain analytical expressions for the most important representations, namely, the P-, Husimi-, and Wigner ones. The behavior of the associated Tsallis entropy is investigated. It is shown that q-values close to two provide the best performance.