Abstract
Because of the dynamical equivalence between the f(R) gravity and the Brans-Dicke theory, the dynamical equation in the f(R) gravity is suggested to be derived from a view point of thermodynamics here. By a conformal transformation, the Brans–Dicke theory in the Jordan frame could be expressed as a minimal coupling scalar field theory in Einstein frame. Using the entropy-area relation [Formula: see text], the correct Friedmann equations could be gotten in both frames. Furthermore, we also discuss the corresponding generalized Misner–Sharp energies for theoretical consistence.
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