Thermodynamical interpretation of gravity in braneworld scenarios

We study the thermodynamical properties of the apparent horizon in the various braneworld scenarios. First, we show that the Friedmann equations can be written directly in the form of the first law of thermodynamics, dE = T(h)dS(h) + W dV, at apparent horizon on the brane, regardless of whether there is the intrinsic curvature term on the brane or a Gauss-Bonnet term in the bulk. This procedure leads to extract an entropy expression in terms of horizon geometry associated with the apparent horizon. Then, we examine the time evolution of the total entropy, including the derived entropy of the apparent horizon and the entropy of the matter fields inside the apparent horizon. We find that the derived entropy of the apparent horizon on the brane satisfies the generalized second law of thermodynamics in braneworld scenarios. These results further support the idea that gravitation on a macroscopic scale is a manifestation of thermodynamics.