  A power-law corrected entropy based on a quantum entanglement is considered
to be a viable black-hole entropy. In this study, as an alternative to
Bekenstein-Hawking entropy, a power-law corrected entropy is applied to
Padmanabhan's holographic equipartition law to thermodynamically examine an
extra driving term in the cosmological equations for a flat
Friedmann-Robertson-Walker universe at late times. Deviations from the
Bekenstein-Hawking entropy generate an extra driving term (proportional to the
$\alpha$-th power of the Hubble parameter, where $\alpha$ is a dimensionless
constant for the power-law correction) in the acceleration equation, which can
be derived from the holographic equipartition law. Interestingly, the value of
the extra driving term in the present model is constrained by the second law of
thermodynamics. From the thermodynamic constraint, the order of the driving
term is found to be consistent with the order of the cosmological constant
measured by observations. In addition, the driving term tends to be
constant-like when $\alpha$ is small, i.e., when the deviation from the
Bekenstein-Hawking entropy is small.
