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It is shown that the differential form of Friedmann equation of a FRWuniverse can be rewritten as a universal form $dE = TdS + WdV$ at apparenthorizon, where $E$ and $V$ are the matter energy and volume inside the apparenthorizon (the energy $E$ is the same as the Misner-Sharp energy in the case ofEinstein general relativity), $W=(\rho-P)/2$ is the work density and $\rho$ and$P$ are energy density and pressure of the matter in the universe,respectively. From the thermodynamic identity one can derive that the apparenthorizon has associated entropy $S= A/4G$ and temperature $T = \kappa / 2\pi$ inEinstein general relativity, where $A$ is the area of apparent horizon and$\kappa$ is the surface gravity at apparent horizon. We extend our procedure tothe Gauss-Bonnet gravity and more general Lovelock gravity and show that thedifferential form of Friedmann equations in these gravities can also berewritten to thee universal form $dE = TdS + WdV$ at the apparent horizon withentropy $S$ being given by expression previously known via black holethermodynamics.Comment: v4: Revtex, 18 pages, to appear in PR

Thermodynamic behavior of the Friedmann equation at the apparent horizon of the FRW universe