Entropic cosmology assumes several forms of entropy on the horizon of the universe , where the entropy can be considered to behave as if it were related to the exchange ( the transfer ) of energy .
To discuss this exchangeability , the consistency of the two continuity equations obtained from two different methods is examined , focusing on a homogeneous , isotropic , spatially flat , and matter-dominated universe .
The first continuity equation is derived from the first law of thermodynamics , whereas the second equation is from the Friedmann and acceleration equations .
To study the influence of forms of entropy on the consistency , a phenomenological entropic-force model is examined , using a general form of entropy proportional to the n -th power of the Hubble horizon .
In this formulation , the Bekenstein entropy ( an area entropy ) , the Tsallis–Cirto black-hole entropy ( a volume entropy ) , and a quartic entropy are represented by n = 2 , 3 , and 4 , respectively .
The two continuity equations for the present model are found to be consistent with each other , especially when n = 2 , i.e. , the Bekenstein entropy .
The exchange of energy between the bulk ( the universe ) and the boundary ( the horizon of the universe ) should be a viable scenario consistent with the holographic principle .