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A power-law corrected entropy based on a quantum entanglement is consideredto be a viable black-hole entropy. In this study, as an alternative toBekenstein-Hawking entropy, a power-law corrected entropy is applied toPadmanabhan's holographic equipartition law to thermodynamically examine anextra driving term in the cosmological equations for a flatFriedmann-Robertson-Walker universe at late times. Deviations from theBekenstein-Hawking entropy generate an extra driving term (proportional to the$\alpha$-th power of the Hubble parameter, where $\alpha$ is a dimensionlessconstant for the power-law correction) in the acceleration equation, which canbe derived from the holographic equipartition law. Interestingly, the value ofthe extra driving term in the present model is constrained by the second law ofthermodynamics. From the thermodynamic constraint, the order of the drivingterm is found to be consistent with the order of the cosmological constantmeasured by observations. In addition, the driving term tends to beconstant-like when $\alpha$ is small, i.e., when the deviation from theBekenstein-Hawking entropy is small.

Thermodynamic constraints on a varying cosmological-constant-like term from the holographic equipartition law with a power-law corrected entropy