title: Friedmann equations and thermodynamics of apparent horizons.
abstract: With the help of a masslike function which has a dimension of energy and is equal to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon dE=T(A)dS(A) can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.
authors.affiliation: College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China. gongyg@cqupt.edu.cn
authors.forename: Yungui
authors.initials: Y
authors.lastname: Gong
authors.forename: Anzhong
authors.initials: A
authors.lastname: Wang