  There are numerous characterizations of Shannon entropy and Tsallis entropy
as measures of information obeying certain properties. Using work by Faddeev
and Furuichi, we derive a very simple characterization. Instead of focusing on
the entropy of a probability measure on a finite set, this characterization
focuses on the `information loss', or change in entropy, associated with a
measure-preserving function. Information loss is a special case of conditional
entropy: namely, it is the entropy of a random variable conditioned on some
function of that variable. We show that Shannon entropy gives the only concept
of information loss that is functorial, convex-linear and continuous. This
characterization naturally generalizes to Tsallis entropy as well.
