Generally the article makes a good impression. However, some additions could be useful for a reader. I believe that an entropy of a flow (Abramov's formula) should be included. It certainly makes sense to communicate to a reader what is a Kolmogorov-Sinai entropy of a dynamical system with continuous time. It seems also useful to include examples of dynamical systems with positive and with zero entropy (e.g. a torus automorphism and rotation of a torus). A fact that KS entropy of a classical deterministic dynamical system is bounded from above could be mentioned together with possible unboundedness of the entropy of a random process.
It is a good article. I have two suggestions. The first one is to mention briefly the Pesin formula for entropy. I also suggest to move the authors remarks about the use of inequality (rather than equality) to the History part of the article.