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.