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

It is shown that the differential form of Friedmann equation of a FRW universe can be rewritten as the first law of thermodynamics dE=TdS+WdV at apparent horizon, where E= is the total energy of matter inside the apparent horizon, V is the volume inside the apparent horizon, W= (-P) /2 is the work density, and P are energy density and pressure of matter in the universe, respectively. From the thermodynamic identity one can derive that the apparent horizon {r}₀ has associated entropy S=A/4G and temperature T=/2 in Einstein general relativity, where A is the area of apparent horizon and is the surface gravity at apparent horizon of FRW universe. We extend our procedure to the Gauss-Bonnet gravity and more general Lovelock gravity and show that the differential form of Friedmann equations in these gravities can also be written as dE=TdS+WdV at the apparent horizon of FRW universe with entropy S being given by expression previously known via black hole thermodynamics.