Observational Modeling of the Kolmogorov-Sinai Entropy

In 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.

Keywords:

Relative entropy , Relative semi-dynamical system , $m_Theta$-equivalence , $m_Theta$-generator , $ (Theta_1 , Theta_2) $-isomorphism