یوسف محمدی

‎In ‎the current study‎, a‎ ‎new ‎type ‎of ‎relative ‎entropy ‎is ‎presented ‎through ‎observable ‎objects ‎in ‎quantum‎ mechanics as the probability measures. The relative probability measures as an extension of probability measures are considered‏ ‎via one-dimensional observers‎‎. ‎The notion of relative entropy of the related to a semi-group on a relative measure space is introduced using the mathematical modeling of an observable object‎. Moreovers‎, ‎it is proved that this non-negative quantity is invariant under $(\Theta_1‎ ,‎\Theta_2 )$-isomorphism‎. Finally‎, ‎we applied this concept to specific semi-groups to extract Kolmogorov entropy of a dynamical system as a special case‎.