A general thermodynamical description of the event horizon in the FRW universe

Abstract: The Friedmann equation in the Friedmann-Robertson-Walker(FRW) universe with any spatial curvature is derived from the first law of thermodynamics on the event horizon. The key idea is to redefine a Hawking temperature on the event horizon. Furthermore, we obtain the evolution equations of the universe including the quantum correction and explore the evolution of the universe in the $f(R)$ gravity. In addition, we also investigate the generalized second law of thermodynamics in Einstein gravity and the $f(R)$ gravity. This perspective also implies that the first law of thermodynamics on the event horizon have a general description in respect of the evolution of the FRW universe.