Observers and Relative Entropy Functional

In this paper, we will use the mathematical modeling of one-dimensional observers to present the notion of the 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 x, where x is the characteristic function on compact metric space x.