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It has been known for some time that there is a deep connection betweenthermodynamics and gravity, with perhaps the most dramatic implication that theEinstein equations can be viewed as a thermodynamic equation of state. RecentlyVerlinde has proposed a model for gravity with a simple statistical mechanicalinterpretation that is applicable in the non-relatvistic regime. Aftercritically analyzing the construction, we present a strong consistency check ofthe model. Specifically, we consider two well-motivated corrections to thearea-entropy relation, the log correction and the volume correction, and followVerlinde's construction to derive corrections to Newton's law of gravitation.We show that the deviations from Newton's law stemming from the log correctionhave the same form as the lowest order quantum effects of perturbative quantumgravity, and the deviations stemming from the volume correction have the sameform as some modified Newtonian gravity models designed to explain theanomalous galactic rotation curves.

Entropic corrections to Newton's law