  We consider a spatially flat Friedmann-Lemaitre-Robertson-Walker space time
and investigate the second law and the generalized second law of thermodynamics
for apparent horizon in generalized modified Gauss Bonnet theory of gravity
(whose action contains a general function of Gauss Bonnet invariant and the
Ricci scalar: $F(R,G)$). By assuming that the apparent horizon is in thermal
equilibrium with the matter inside it, conditions which must be satisfied by
$F(R,G)$ are derived and elucidated through two examples: a quasi-de Sitter
space-time and a universe with power law expansion.
