  Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent
horizon of a FRW universe, and assuming that the associated entropy with
apparent horizon has a quantum corrected relation, $S=\frac{A}{4G}-\alpha \ln
\frac{A}{4G}+\beta \frac{4G}{A}$, we derive modified Friedmann equations
describing the dynamics of the universe with any spatial curvature. We also
examine the time evolution of the total entropy including the quantum corrected
entropy associated with the apparent horizon together with the matter field
entropy inside the apparent horizon. Our study shows that, with the local
equilibrium assumption, the generalized second law of thermodynamics is
fulfilled in a region enclosed by the apparent horizon.
