  Cosmological equations were recently derived by Padmanabhan from the
expansion of cosmic space due to the difference between the degrees of freedom
on the surface and in the bulk in a region of space. In this study, a modified
R\'{e}nyi entropy is applied to Padmanabhan's `holographic equipartition law',
by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy
and using a logarithmic formula of the original R\'{e}nyi entropy.
Consequently, the acceleration equation including an extra driving term (such
as a time-varying cosmological term) can be derived in a homogeneous,
isotropic, and spatially flat universe. When a specific condition is
mathematically satisfied, the extra driving term is found to be constant-like
as if it is a cosmological constant. Interestingly, the order of the
constant-like term is naturally consistent with the order of the cosmological
constant measured by observations, because the specific condition constrains
the value of the constant-like term.
