  An explosive percolation transition is the abrupt emergence of a giant
cluster at a threshold caused by a suppression of the growth of large clusters.
In this paper, we consider the information entropy of the cluster size
distribution, which is the probability distribution for the size of a randomly
chosen cluster. It has been reported that information entropy does not reach
its maximum at the threshold in explosive percolation models, a result
seemingly contrary to other previous results that the cluster size distribution
shows power-law behavior and the cluster size diversity (number of distinct
cluster sizes) is maximum at the threshold. Here, we show that this phenomenon
is due to that the scaling form of the cluster size distribution is given
differently below and above the threshold. We also establish the scaling
behaviors of the first and second derivatives of the information entropy near
the threshold to explain why the first derivative has a negative minimum at the
threshold and the second derivative diverges negatively (positively) at the
left (right) limit of the threshold, as predicted through previous simulation.
