REGULARIZATION OF QUANTUM RELATIVE ENTROPY IN FINITE DIMENSIONS AND APPLICATION TO ENTROPY PRODUCTION

The fundamental concept of relative entropy is extended to a functiona l that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost al l important properties of ordinary relative entropy such as joint conv exity and contractivity under completely positive quantum dynamical se migroup time evolution. On this basis a generalized formula for entrop y production is proposed, the applicability of which is tested in mode ls of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves al l types of states.