  It has been shown that Friedmann equation of FRW universe can be derived from
the idea which says cosmic space is emergent as cosmic time progresses and our
universe is expanding towards the state with the holographic equipartition by
Padmanabhan. In this note, we give a general relationship between the horizon
entropy and the number of the degrees of freedom on the surface, we also obtain
the corresponding dynamic equations by using the idea of emergence of space in
the $f(R)$ theory and deformed Ho\v{r}ava-Lifshitz (HL) theory.
