Dynamical entropy of generalized quantum Markov chains

We compute the dynamical entropy in the sense of Connes, Narnhofer, and Thirring of shift automorphism of generalized quantum Markov chains as defined by Accardi and Frigerio. For any generalized quantum Markov chain defined via a finite set of conditional density amplitudes, we show that the dynamical entropy is equal to the mean entropy.Research supported in part by the Basic Science Research Program, Korean Ministry of Education, 1993–1994.