Bekenstein bound on black hole entropy in non-Gaussian statistics

TL;DR

This paper explores how the Bekenstein bound on black hole entropy is affected by non-Gaussian statistical frameworks and finds that incorporating GUP effects can restore the bound's validity.

Contribution

It demonstrates the violation of the standard Bekenstein bound in non-Gaussian statistics and proposes a generalized bound that accounts for GUP effects, linking entropy indices with quantum gravity parameters.

Findings

Standard Bekenstein bound violated in non-Gaussian statistics

Generalized bound satisfied when GUP effects are included

Possible connection between entropy indices and GUP parameter

Abstract

The Bekenstein bound, inspired by the physics of black holes, is introduced to constrain the entropy growth of a physical system down to the quantum level in the context of a generalized second law of thermodynamics. We first show that the standard Bekenstein bound is violated when the entropy of a Schwarzschild black hole is described in non-Gaussian statistics Barrow, Tsallis, and Kaniadakis due to the presence of the related indices $\Delta$, $q$ and $\kappa$, respectively. Then, by adding the GUP effects into the Bekenstein bound, we find that the generalized bound is satisfied in the context of the mentioned entropies through a possible connection between the entropies indices and the GUP parameter $\beta$.