Tesallis entropy in the Husimi and Wigner representations

In this paper the Tesallis entropy is developed into the phase space picture of quantum mechanics, for an ordinary range of q-parameters. We apply the Tesallis entropy for the Schrodinger Cat State (SCS) in the Husimi and Wigner representations. It will reduce to the Whrel and linear entropies for a corresponding q-parameter. The variations of the Tesallis entropy in terms of the nonlinear effect and strong field for the SCS are compared with the corresponding SCS quantum signature which is introduced by Kenfack et al. We find a suitable q-parameter for the Tesallis entropy which has a best fitting with the quantum signature.