  In this article, we investigate the assumption of equipartition of energy in
arguments for the entropic nature of gravity. It has already been pointed out
by other authors that equipartition is not valid for low temperatures. Here we
additionally point out that it is similarly not valid for systems with bounded
energy. Many explanations for black hole entropy suggest that the microscopic
systems responsible have a finite dimensional state space, and thus finite
maximum energy. Assuming this to be the case leads to drastic corrections to
Newton's law for high gravitational fields, and, in particular, to a
singularity in acceleration at finite radius away from a point mass. This is
suggestive of the physics at the Schwarzschild radius. We show, however, that
the location of the singularity scales differently.
