Time evolution of quasi-hermitian open systems and generalized entropy functional

Abstract

We study general properties of dynamical maps preserving Hermiticity and quasi-Hermiticity, and prove that the generator of a dynamical semigroup is always a pseudo-Hermitian operator. Moreover, improving a previous proposal by Jakob and Stenholm, we introduce two new Lyapunov functionals for degenerate open systems, and apply such results to a physical example.