Entropy functionals of Kolmogorov-Sinai type and their limit theorems (Q1912356)

The authors introduce two functionals \(S\) and \(T\) for \(C^*\)-dynamical systems with invariant states and stationary channels. They show that \(S\) and \(T\) satisfy theorems of the Kolmogorov-Sinai type. In fact, within the framework of quantum information theory, as formulated in the operator algebraic setting by \textit{M. Ohya} [Rep. Math. Phys. 27, 19-47 (1987; Zbl 0709.94011)], these functionals extend the quantum Kolmogorov-Sinai entropy introduced by \textit{A. Connes}, \textit{H. Narnhofer} and \textit{W. Thirring} [Commun. Math. Phys. 112, 691-791 (1987; Zbl 0637.46073)] and the mutual entropy due to \textit{M. Ohya} [IEEE Trans. Inform. Theory 29, 770-774 (1983; Zbl 0511.94007)].