Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law

摘要

In this work, we have illustrated the difference between both Tsallis andKaniadakis entropies through cosmological models obtained from the formalismproposed by Padmanabhan, which is called holographic equipartition law. Similarto the formalism proposed by Komatsu, we have obtained an extra drivingconstant term in the Friedmann equation if we deform the Tsallis entropy byKaniadakis' formalism. We have considered initially Tsallis entropy as theBlack Hole (BH) area entropy. This constant term may lead the universe to be inan accelerated mode. On the other hand, if we start with the Kaniadakis entropyas the BH area entropy and then by modifying the Kappa expression by Tsallis'formalism, the same constant, which shows that the universe have anacceleration was obtained. In an opposite limit, no driving inflation term ofthe early universe was derived from both deformations.