On the Entropy of Dynamical Systems on σ −mv-Algebras with State
Mohammad Ebrahimi, Uosef Mohammadi, Roya Ghasemkhani · 2015
One of the important concepts in physics and mathematics is entropy. The present paper deals with the theory of entropy using the Loomis-Sikorski representation of σ −MV -algebras. In this paper the conditional entropy of a finite partition ξ given �� by use of conditional expectation on σ −MV-algebras when �� is an arbitrary sub− σ −MV -algebra of the σ −MV –algebra �� is defined. It is shown that the mean entropy of an MVdynamical system is affine. Also the concept of a subsystem of an MV-dynamical system is introduced and the relation between their entropies is investigated.