  Completely positive transformations play an important role in the description
of state changes in quantum mechanics, including the time evolution of open
quantum systems. One useful tool to describe them is the so-called Choi
isomorphism, which maps completely positive transformations to positive
semi-definite matrices. Accordingly, there are numerous proposals to generalize
the Choi isomorphism. In the present paper, we show that the 1976 paper of
Gorini, Kossakowski and Sudarshan (GKS) already holds the key for a further
generalization and study the resulting GKS isomorphism. As an application, we
compute the GKS matrix of the time evolution of a general open quantum system
up to second order in time.
