On the entropic derivation of the $r^{-2}$ Newtonian gravity force

Abstract

Following Verlinde's conjecture, we show that Tsallis' classical free particle distribution at temperature $T$ can generate Newton's gravitational force's $r^{-2}$ {\it distance's dependence}. If we want to repeat the concomitant argument by appealing to either Boltzmann-Gibbs' or Renyi's distributions, the attempt fails and one needs to modify the conjecture. Keywords: Tsallis', Boltzmann-Gibbs', and Renyi's distributions, classical partition function, entropic force.