  It is possible to obtain the gravitational field equations in a large class
of theories from a thermodynamic variational principle which uses the
gravitational heat density $\mathcal{S}_g$ associated with null surfaces. This
heat density is related to the discreteness of spacetime at Planck scale,
$L_P^2 = (G\hbar / c^3)$, which assigns $A_{\perp}/L_P^2$ degrees of freedom to
any area $A_{\perp}$. On the other hand, it is also known that the surface term
$K\sqrt{h}$ in the gravitational action principle correctly reproduces the heat
density of the null surfaces. We provide a link between these ideas by
obtaining $\mathcal{S}_g$, used in emergent gravity paradigm, from the surface
term in the action in Einstein's gravity. This is done using the notion of a
nonlocal qmetric -- introduced recently [arXiv:1307.5618, arXiv:1405.4967] --
which allows us to study the effects of zero-point-length of spacetime at the
transition scale between quantum and classical gravity. Computing $K\sqrt{h}$
for the qmetric in the appropriate limit directly reproduces the entropy
density $\mathcal{S}_g$ used in the emergent gravity paradigm.
