Relative entropy of states of von Neumann algebras
Relative entropy \(S(\varphi/\psi)\) of two faithful normal positive linear functionals \(\varphi\) and \(\psi\) of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy under restriction to subalgebras are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved in the context of von Neumann algebras. The definition and the results about relative entropy has been since extended to non-faithful \(\varphi\) and \(\psi\) as well as to the case of \(C^*\)-algebras.
scientific article; zbMATH DE number 3511002