Does Holographic equipartition demand a pure cosmological constant?

The spacial expansion of the universe could be described as a tendency for satisfying holographic equipartition which inevitably demands the presence of dark energy. We explore whether this novel idea proposed by Padmanabhan give any additional insights into the nature of dark energy. In particular, we obtain the constraints imposed by the law of emergence on the equation of state parameter, $\omega$. We also present a thermodynamic motivation for the obtained constraints on $\omega$. Further, we explicitly prove the feasibility of describing a dynamic dark energy model through the law of emergence. Interestingly, both holographic equipartition and the entropy maximization demands an asymptotically de Sitter universe with $\omega\geq-1$, rather than a pure cosmological constant.