Holographic considerations on non-gaussian statistics and gravothermal catastrophe

•Comparison of Tsallis and Kaniadakis statistical formalisms.•Use of the Verlinde’s holographic approach.•Gravothermal catastrophe phenomena analyzed.

In this paper we have derived the equipartition law of energy using Tsallis formalism and the Kaniadakis power law statistics in order to obtain a modified gravitational constant. We have applied this result in the gravothermal collapse phenomenon. We have discussed the equivalence between Tsallis and the Kaniadakis statistics in the context of Verlinde’s entropic formalism. In the same way we have analyzed the negative heat capacities in the light of gravothermal catastrophe. The relative deviations of the modified gravitational constants are derived.