Spatial cut-offs, Fermion Statistics, and Verlinde's Conjecture

Abstract: Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in [Physica A {\bf 505} (2018) 190] within a purely classical statistical context, and in [DOI: 10.13140/RG.2.2.34454.24640] for the case of bosons' statistics. In the present work, we appeal to a quantum scenario involving fermions' statistics. We consider also the classical limit of quantum (statistical) mechanics (QM). We encounter a lower bound to the distance $r$ between the two interacting masses, i.e., an $r$ cut-off. This is a new effect that exhibits some resemblance with the idea of space discretization proposed by recent gravitation theories