  We define a new quantitative measure for an arbitrary factorial language: the
entropy of a random walk in the prefix tree associated with the language; we
call it Markov entropy. We relate Markov entropy to the growth rate of the
language and to the parameters of branching of its prefix tree. We show how to
compute Markov entropy for a regular language. Finally, we develop a framework
for experimental study of Markov entropy by modelling random walks and present
the results of experiments with power-free and Abelian-power-free languages.
