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Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the totalentropy of a gravitational system should be related to the volume of systeminstead of the system surface. Here, we show that this new proposal cannotsatisfy the unified first law of thermodynamics and the Friedmans equationsimultaneously, unless the effects of dark energy candidate on the horizonentropy are considered. In fact, our study shows that some types of dark energycandidate may admit this proposal. Some general properties of required darkenergy are also addressed. Moreover, our investigation shows that this newproposal for entropy, while combined with the second law of thermodynamics (asthe backbone of Verlinde's proposal), helps us in providing a thermodynamicinterpretation for the difference between the surface and bulk degrees offreedom which, according to Padmanabhan's proposal, leads to the emergence ofspacetime and thus the universe expansion. In fact, our investigation showsthat the entropy changes of system may be equal to the difference between thesurface and bulk degrees of freedom falling from surface into the systemvolume. Briefly, our results signal us that this new proposal for entropy maybe in agreement with the thermodynamics laws, the Friedmann equation,Padmanabhan's holographic proposal for the emergence of spacetime and thereforethe universe expansion. In fact, this new definition of entropy may be used tomake a bridge between Verlinde's and Padmanabhan's proposals.

Implications, consequences and interpretations of generalized entropy in the cosmological setups