Derivation of Tsallis statistics from dynamical equations for a granular gas

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.