Macroscopic cell representation of density matrix equation and optimal choice of projectors by variational principle

We introduce a complete set of projectors on Liouvillespace and a “cell representation” of the equation of motion of the density matrixρ adjusted to the macroscopic observables of the system. Using a variational principle, the projector on the relevant density matrixρ _rel is determined by the postulate that the subdynamics ofρ _rel should include an optimal part of the Liouvillean?. The relation of the reduced subdynamics equation to wellknown master equations is investigated.