Thermodynamic Behavior of Friedmann Equations at Apparent Horizon of FRW Universe

It is shown that the differential form of Friedmann equations of a FRW universe can be rewritten as a thermodynamical identity T dS = dE + P dV at apparent horizon, where E is the Misner-Sharp energy, V is the volume inside the apparent horizon, and P is the pressure of the perfect fluid in the universe. From the thermodynamic identity one can derive that the apparent horizoñ r A has associated temperature T = 1/2π˜r A and entropy S = A/4G in Einstein general relativity, where A is the area of apparent horizon. We extend our procedure to the Gauss-Bonnet gravity and more general Lovelock gravity and show that the field equations in these gravities can also be identified as a thermodynamical system satisfying T dS = dE + P dV at the apparent horizon of FRW universe with entropy S being given by expression previously known via black hole thermodynamics.