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

¹ Grupo de Física Teórica e Matemática Física, Departamento de Física, Universidade Federal Rural do Rio de Janeiro 23890-971, Seropédica, RJ, Brazil
² Departamento de Física, Universidade Federal de Juiz de Fora - 36036-330, Juiz de Fora, MG, Brazil

^(a) evertonabreu@ufrrj.br
^(b) jorge@fisica.ufjf.br
^(c) albert@fisica.ufjf.br
^(d) abonillafisica.ufjf.br

Received: 15 December 2017
Accepted: 30 March 2018

Abstract

In this work, we have illustrated the difference between both Tsallis and Kaniadakis entropies through cosmological models obtained from the formalism proposed by Padmanabhan, which is called holographic equipartition law. Similarly to the formalism proposed by Komatsu, we have obtained an extra driving constant term in the Friedmann equation if we deform the Tsallis entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy as the black-hole (BH) area entropy. This constant term may lead the universe to be in an accelerated or decelerated mode. On the other hand, if we start with the Kaniadakis entropy as the BH area entropy and then by modifying the Kappa expression by Tsallis' formalism, the same absolute value but with opposite sign is obtained. In an opposite limit, no driving inflation term of the early universe was derived from both deformations.