Exploring modified Kaniadakis entropy: MOND-related theory, the Bekenstein bound conjecture, and Hawking evaporation within the Landauer principle

TL;DR

This paper explores a modified Kaniadakis entropy framework to describe black-hole thermodynamics, its connection to MOND, the Bekenstein bound, and black hole evaporation, highlighting its potential across various physics domains.

Contribution

It introduces a modified Kaniadakis entropy model that links black-hole thermodynamics with MOND and the Bekenstein bound, offering new insights into quantum and gravitational phenomena.

Findings

Kaniadakis entropy can describe black-hole entropy accurately.

The Bekenstein bound holds for typical Kaniadakis parameters.

Derived a mass loss expression for black hole evaporation using Landauer principle.

Abstract

We investigate the description of black-hole thermodynamics in terms of a recently proposed modified version for Kaniadakis entropy. We discuss the role of that proposal within the Modified Newtonian Dynamics (MOND) theory, a generalization of Newton's second law aimed at explaining galaxy rotation curves without resorting to dark matter. We posit a conjecture that the Kaniadakis entropy precisely describes the Bekenstein-Hawking black-hole entropy. Furthermore, we consider the Bekenstein bound conjecture which imposes an upper limit on the entropy of confined quantum systems. We analyze that conjecture in the context of the modified Kaniadakis entropy and find that it holds for typical values of $\kappa$, as evidenced by our numerical investigation. Finally, using the Landauer principle from information theory, we derive an expression for mass loss in black hole evaporation. Our exploration underscores the potential relevance of a modified Kaniadakis statistics in understanding diverse physical phenomena, from gravitational systems to quantum mechanics, offering a promising direction for future research at the intersection among statistical mechanics and a continually increasing number of other important areas of physics.