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

Abstract: In a 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.