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

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.