  We introduce the concept of inflation word entropy for random substitutions
with a constant and primitive substitution matrix. Previous calculations of the
topological entropy of such systems implicitly used this concept and
established equality of topological entropy and inflation word entropy, relying
on ad hoc methods. We present a unified scheme, proving that inflation word
entropy and topological entropy in fact coincide. The topological entropy is
approximated by a converging series of upper and lower bounds which, in many
cases, lead to an analytic expression.
