Gauss-Bonnet and Lovelock Gravities and the Generalized Second Law of Thermodynamics

It has been shown Chin.Phys.Lett.25(2008)4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss--Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature associated with the apparent horizon of a Friedman-Robertson-Walker (FRW) universe and assuming T_m=bT_h, we are able to construct conditions for which the generalized second law holds in Gauss-Bonnet and Lovelock gravities, where T_m and T_h are the temperatures of the source and the horizon respectively.