Tsallis Entropy of Product MV-Algebra Dynamical Systems

Entropy

Dagmar Markechová¹  Beloslav Riečan² 

[1] Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia;Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica, Slovakia;

关键词: product MV-algebra;    partition;    Tsallis entropy;    conditional Tsallis entropy;    dynamical system;   

DOI  :  10.3390/e20080589

来源: DOAJ

【 摘 要 】

This paper is concerned with the mathematical modelling of Tsallis entropy in product MV-algebra dynamical systems. We define the Tsallis entropy of order α , where α ∈ ( 0 , 1 ) ∪ ( 1 , ∞ ) , of a partition in a product MV-algebra and its conditional version and we examine their properties. Among other, it is shown that the Tsallis entropy of order α , where α > 1 , has the property of sub-additivity. This property allows us to define, for α > 1 , the Tsallis entropy of a product MV-algebra dynamical system. It is proven that the proposed entropy measure is invariant under isomorphism of product MV-algebra dynamical systems.

【 授权许可】

Unknown