Statistical mechanics of the self-gravitating gas in the Tsallis framework

The statistical mechanics of a cloud of particles interacting via their gravitational potentials encounters some issues when the Boltzmann-Gibbs statistics is applied. In this work, we consider the alternative statistical framework of Tsallis and analyze the statistical and thermodynamical implications for a self-gravitating gas, obtaining analytical and convergent expressions for the equation of state and specific heat in the ensembles of constant temperature and constant energy. Although our results are comparable in both ensembles, it turns out that only in the ensemble of constant temperature do the thermodynamic quantities depend explicitly on the Tsallis parameter, indicating that the question of ensemble equivalence for Tsallis statistics must be further reviewed.