Rényi Entropies of Dynamical Systems: A Generalization Approach

Entropy measures have received considerable attention in quantifying the structural complexity of real-world systems and are also used as measures of information obtained from a realization of the con-sidered experiments. In the present study, new notions of entropy for a dynamical system are introduced. The R´enyi entropy of measurable partitions of order q ∈ (0, 1) ∪ (1, ∞) and its conditional version are defined, and some important properties of these concepts are studied. It is shown that the Shannon entropy and its conditional version for mea-surable partitions can be obtained as the limit of their R´enyi entropy and conditional R´enyi entropy. In addition, using the suggested concept of R´enyi entropy for measurable partitions, the R´enyi entropy for dynam-ical systems is introduced. It is also proved that the R´enyi entropy for dynamical systems is invariant under isomorphism.