  In this work we present the explicit calculation of Probability Distribution
Function for a model system of granular gas within the framework of Tsallis
Non-Extensive Statistical Mechanics, using the stochastic approach by Beck [C.
Beck, Phys. Rev. Lett. 87, 180601 (2001)], further generalized by Sattin and
Salasnich [F. Sattin and L. Salasnich, Phys. Rev. E 65, 035106(R) (2002)]. The
calculation is self-consistent in that the form of Probability Distribution
Function is not given as an ansatz but is shown to necessarily arise from the
known microscopic dynamics of the system.

Statistical Mechanics