  In this paper, we show how the entropy (including the von Neumann entropy
obtained by tracing across various sizes of subsystems, the entanglement gap,
as well as different degrees of R\'{e}nyi entropy) of the random reduced
density matrices are related to their dominant eigenvalue. Analytical results
are deduced from Random Matrix Theory (RMT) for decentralized Wishart matrices
and backed up by computer simulations. The correlation between our study and
entanglement generated by quantum computing is provided with various examples.
