The Renyi α-entropy of a random variable with some probability distribution q is defined to be H α (q) = α 1−α log q α and there are two useful results we use (Principe, 2010): 1) lim α→1 H α (q) = H(q), where H(q) is the Shannon entropy; and 2) H α (q) is non-increasing in α.
for α < 1, H α (q) is an upper bound on the Shannon entropy.