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.