  We share a small connection between information theory, algebra, and topology
- namely, a correspondence between Shannon entropy and derivations of the
operad of topological simplices. We begin with a brief review of operads and
their representations with topological simplices and the real line as the main
example. We then give a general definition for a derivation of an operad in any
category with values in an abelian bimodule over the operad. The main result is
that Shannon entropy defines a derivation of the operad of topological
simplices, and that for every derivation of this operad there exists a point at
which it is given by a constant multiple of Shannon entropy. We show this is
compatible with, and relies heavily on, a well-known characterization of
entropy given by Faddeev in 1956 and a recent variation given by Leinster.
