  A systematic approach to the non-Markovian quantum dynamics of open systems
is given by the projection operator techniques of nonequilibrium statistical
mechanics. Combining these methods with concepts from quantum information
theory and from the theory of positive maps, we derive a class of correlated
projection superoperators that take into account in an efficient way
statistical correlations between the open system and its environment. The
result is used to develop a generalization of the Lindblad theory to the regime
of highly non-Markovian quantum processes in structured environments.
