University of MaraghehSahand Communications in Mathematical Analysis2322-580713120190201Observational Modeling of the Kolmogorov-Sinai Entropy1011142998310.22130/scma.2018.29983ENUosefMohammadiDepartment of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran.Journal Article20170120In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical systems are investigated. Also, a relative version of Kolmogorov-Sinai theorem is given. Finally, it is proved that the relative entropy of a relative $ Theta $-measure preserving transformations with respect to a relative sub-$sigma_Theta$-algebra having finite atoms is affine.https://scma.maragheh.ac.ir/article_29983_7a5face43ae162c0c5d62beecf8dc888.pdf