Rényi Entropies of Dynamical Systems: A Generalization Approach

Document Type : Research Paper

Authors

1 Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran

2 Department of Economics, Sirjan Branch, Islamic Azad University, Sirjan, Iran

Abstract

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 considered experiments. In the present study, new notions of entropy for a dynamical system are introduced. The Rényi entropy of measurable partitions of order 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 measurable partitions can be obtained as the limit of their Rényi entropy and conditional Rényi entropy. In addition, using the suggested concept of Rényi entropy for measurable partitions, the Rényi entropy for dynamical systems is introduced. It is also proved that the Rényi entropy for dynamical systems is invariant under isomorphism.

Keywords

References

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History

  • Receive Date: 09 September 2021
  • Revise Date: 11 April 2022
  • Accept Date: 21 May 2022

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