Tsallis entropy of dynamical systems – a general scheme

Article type: Research Article

Authors: Ebrahimzadeh, Abolfazl^{a; *} | Eslami Giski, Zahra^b

Affiliations: [a] Department of Mathematics, Zahedan Branch, Islamic Azad University, Zahedan, Iran | [b] Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran

Correspondence: [*] Corresponding author. Abolfazl Ebrahimzadeh. Tel.: +98 9159619270; Fax: +98 5431135244; E-mail: a.ebrahimzade@iauzah.ac.ir.

Abstract: In the papers by Riecan et al. (Fuzzy Sets Syst. 96, 1998) and Ebrahimzadeh et al. (Mathematics, 5, 2017) some fuzzy modifications of Shannon and logical entropy have been studied and the general scheme involving the presented models has been introduced. The present paper deals with providing analogies of these results for the case of Tsallis entropy. In particular, chain rules and concavity property for Tsallis entropy of partitions on the appropriate algebraic structure are established. Using the concept of Tsallis entropy of partitions, we define Tsallis entropy of dynamical systems and prove concavity property of Tsallis entropy of dynamical systems. Finally, we prove the version of Kolmogorov-Sinai Theorem for Tsallis entropy.

Keywords: Tsallis entropy, M-preserving transformation, dynamical system, generator

DOI: 10.3233/JIFS-17901

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 1, pp. 1119-1126, 2018