Observers and Relative Entropy Functional
Subject Areas : International Journal of Industrial Mathematics
عادل گروهی
1
(
Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.
)
یوسف محمدی
2
(
Department of Mathematics, University of Jiroft, Jiroft, Iran.
)
محمد ابراهیمی
3
(
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
)
Keywords: Relative entropy functional, Kolmogorov entropy, Invariant, Relative dynamical system,
Abstract :
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 $X$.
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