  There is considerable evidence to suggest that the field equations of gravity
have the same status as, say, the equations describing an emergent phenomenon
like elasticity. In fact, it is possible to derive the field equations from a
thermodynamic variational principle in which a set of normalized vector fields
are varied rather than the metric. We show that this variational principle can
arise as a low energy ($L_P = (G\hbar/c^3)^{1/2} \to 0$) relic of a plausible
nonperturbative effect of quantum gravity, viz. the existence of a
zero-point-length in the spacetime. Our result is nonperturbative in the
following sense: If we modify the geodesic distance in a spacetime by
introducing a zero-point-length, to incorporate some effects of quantum
gravity, and take the limit $L_P \to 0$ of the Ricci scalar of the modified
metric, we end up getting a nontrivial, leading order ($L_P$ - independent)
term. \textit{This term is identical to the expression for entropy density of
spacetime used previously in the emergent gravity approach.} This reconfirms
the idea that the microscopic degrees of freedom of the spacetime, when
properly described in the full theory, could lead to an effective description
of geometry in terms of a thermodynamic variational principle. This is
conceptually similar to the emergence of thermodynamics from mechanics of, say,
molecules. The approach also has important implications for cosmological
constant which are briefly discussed.
