عادل گروهی - Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
یوسف محمدی - Department of Mathematics, University of Jiroft, Jiroft, ‎Iran‎.
محمد ابراهیمی - Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, ‎Iran‎.

‎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.

Kolmogorov entropy, Relative dynamical system, Invariant, Relative entropy ‎functional‎