On the Interrelation of the Generalized Holographic Equipartition and Entropy Maximization in Kaniadakis Paradigm

TL;DR

This paper explores the relationship between generalized holographic equipartition and horizon entropy maximization within a Kaniadakis entropy framework in a non-flat universe, confirming their compatibility.

Contribution

It demonstrates the compatibility of holographic equipartition with Kaniadakis entropy maximization in curved cosmological models, extending previous entropy-based analyses.

Findings

Horizon entropy maximization conditions derived for Kaniadakis entropy.

Holographic equipartition is consistent with horizon entropy maximization.

Results apply to non-flat Friedmann-Robertson-Walker universes.

Abstract

This study examines the compatibility of the generalized holographic equipartition proposed in ref \cite{sheykhi2013friedmann} with the maximization of horizon entropy in an (n + 1)-dimensional non-flat Friedmann-Robertson-Walker (FRW) universe. Here, the entropy associated with the apparent horizon is described by Kaniadakis entropy, as well as truncated Kaniadakis entropy, which is expanded and truncated to third order when the Kaniadakis parameter $(K)$ is small, indicating minor deviations from the standard Bekenstein-Hawking entropy. Initially, we derive the conditions required for maximizing both Kaniadakis horizon entropy and truncated Kaniadakis horizon entropy. We then examine whether the generalized holographic equipartition aligns with the constraints of horizon entropy maximization. Our findings reveal that the generalized holographic equipartition is consistent with the maximization of Kaniadakis horizon entropy and truncated Kaniadakis horizon entropy in a universe with non-zero spatial curvature.