  Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the total
entropy of a gravitational system should be related to the volume of system
instead of the system surface. Here, we show that this new proposal cannot
satisfy the unified first law of thermodynamics and the Friedmans equation
simultaneously, unless the effects of dark energy candidate on the horizon
entropy are considered. In fact, our study shows that some types of dark energy
candidate may admit this proposal. Some general properties of required dark
energy are also addressed. Moreover, our investigation shows that this new
proposal for entropy, while combined with the second law of thermodynamics (as
the backbone of Verlinde's proposal), helps us in providing a thermodynamic
interpretation for the difference between the surface and bulk degrees of
freedom which, according to Padmanabhan's proposal, leads to the emergence of
spacetime and thus the universe expansion. In fact, our investigation shows
that the entropy changes of system may be equal to the difference between the
surface and bulk degrees of freedom falling from surface into the system
volume. Briefly, our results signal us that this new proposal for entropy may
be in agreement with the thermodynamics laws, the Friedmann equation,
Padmanabhan's holographic proposal for the emergence of spacetime and therefore
the universe expansion. In fact, this new definition of entropy may be used to
make a bridge between Verlinde's and Padmanabhan's proposals.
