Observers and Relative ‎E‎ntropy ‎Functional‎

‎In this paper‎, ‎we will use the mathematical modeling of one-dimensional observers to present the notion of the \emph{relative entropy functional} for relative dynamical systems‎. ‎Also‎, ‎the invariance of the entropy of a system under topological conjugacy is generalized to the relative entropy functional‎. ‎Moreover‎, ‎from observer viewpoint‎, ‎a new version of the Jacobs Theorem is obtained‎. ‎It has been proved that relative entropy functional is equivalent to the Kolmogorov entropy for dynamical systems‎, ‎from the viewpoint of observer \chi_X ‎, ‎where \chi_X is the characteristic function on compact metric space X‎.

کلیدواژه ها:

Kolmogorov entropy ، Relative dynamical system ، Invariant ، Relative entropy ‎functional‎