  Following Chakrabarti,Chandrasekhar, and Naina [Physica A {\bf 389} (2010)
1571], we attempt a classical relativistic treatment of Verlinde's emergent
entropic force conjecture by appealing to a relativistic Hamiltonian in the
context of Tsalli's statistics. The ensuing partition function becomes the
classical one for small velocities. We show that Tsallis' relativistic
(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 Renyi's distribution, the
attempt fails and one needs to modify the conjecture.

Statistical Mechanics;General Relativity and Quantum Cosmology