  Recently, it was argued that the spacetime dynamics can be understood by
calculating the difference between the degrees of freedom on the boundary and
in the bulk in a region of space. In this Letter, we apply this new idea to
braneworld scenarios and extract the corresponding Friedmann equations of
$(n-1)$-dimensional brane embedded in the $(n+1)$-dimensional bulk with any
spacial curvature. We will also extend our study to the more general
Gauss-Bonnet braneworld with curvature correction terms on the brane and in the
bulk, and derive the dynamical equation in a nonflat Universe.
