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

TL;DR

This paper compares Tsallis and Kaniadakis entropies within cosmological models based on the holographic equipartition law, revealing how different entropy deformations influence cosmic acceleration and the universe's expansion dynamics.

Contribution

It introduces a novel analysis of Tsallis and Kaniadakis entropies in cosmology, demonstrating their effects on the Friedmann equations and universe acceleration through a holographic framework.

Findings

Deformation of Tsallis entropy yields an acceleration-driving constant in the Friedmann equation.

Deformation of Kaniadakis entropy also produces a similar acceleration term.

No inflation-driving term is found in early universe scenarios from these deformations.

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 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 constant, which shows that the universe have an acceleration is obtained. In an opposite limit, no driving inflation term of the early universe was derived from both deformations.