A Note on and Generalization of "Exploring Modified Kaniadakis Entropy: MOND Theory and the Bekenstein Bound Conjecture"

TL;DR

This paper generalizes the derivation of MOND phenomenology from entropic gravity by demonstrating that various non-Boltzmann-Gibbs entropies, beyond Kaniadakis', can lead to similar gravitational behavior under certain conditions.

Contribution

It introduces a broader framework showing that MOND-like gravity emerges from a wide class of generalized entropies, extending previous results based on Kaniadakis entropy.

Findings

MOND behavior arises from various non-Boltzmann-Gibbs entropies

The derivation depends on minimal conditions on the entropy function

Generalized entropies can reproduce gravitational phenomenology similar to MOND

Abstract

In a recent paper by Ambr\'osio et al. [arXiv:2405.14799], it was shown that the gravitational force law of the Modified Newtonian Dynamics (MOND) phenomenology can be derived within the framework of entropic gravity and the holographic principle by assuming an entropy function other than the conventional Boltzmann-Gibbs entropy. In particular, they derived the standard interpolation function of MOND together with an analytical expression for the acceleration constant $a_0$ by utilizing Kaniadakis' modified entropy. In this short note, using the same methodology, we generalize this result and show that MONDian behavior is a rather general consequence of combining entropic gravity with non-Boltzmann-Gibbs entropies, which depends on only a few conditions imposed on the generalized entropy function.