  In the paper, hep-th/0501055 (R.G. Cai and S.P. Kim, JHEP {\bf 0502}, 050
(2005)), it is shown that by applying the first law of thermodynamics to the
apparent horizon of an FRW universe and assuming the geometric entropy given by
a quarter of the apparent horizon area, one can derive the Friedmann equations
describing the dynamics of the universe with any spatial curvature; using the
entropy formula for the static spherically symmetric black holes in
Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is
not proportional to the horizon area, one can also obtain the corresponding
Friedmann equations in each gravity. In this note we extend the study of
hep-th/0501055 to the cases of scalar-tensor gravity and $f(R)$ gravity, and
discuss the implication of results.
