On certain properties of the relative entropy of states of operator algebras
Several properties of the relative entropy S(\(\phi\),\(\omega\)) of the states \(\phi\) and \(\omega\) of a \(C^*\)-algebra are established. It is proven that \(S(\phi,\omega)=S(\phi | {\mathcal A}_ 1,\omega | {\mathcal A}_ 1)| S(\omega \circ E,\omega)\) if \({\mathcal A}_ 1\), \({\mathcal A}\) are \(C^*\)-algebras and E is a \(\phi\)-preserving conditional expectation onto \({\mathcal A}_ 1\). A fairly general version of the strong superadditivity is obtained and used to prove the existence of the mean relative entropy for an abstract noncommutative stationary Markov chain.
existence of the mean relative entropy for an abstract noncommutative stationary Markov chain
scientific article; zbMATH DE number 1001
scientific article