  Shannon entropy is widely used to quantify the uncertainty of discrete random
variables. But when normalized to the unit interval, as is often done in
practice, it no longer conveys the alphabet sizes of the random variables being
studied. This work introduces an entropy functional based on Jensen-Shannon
divergence that is naturally bounded from above by one. Unlike normalized
Shannon entropy, this new functional is strictly increasing in alphabet size
under uniformity and is thus well suited to the characterization of discrete
random variables.
