Projection formalism in the theory of irreversible processes

A modification is proposed in the formalism of the Brussels school in conjugation with the projection technique; this considerably simplifies the proof of the main results of the theory. The method is used to construct a macroscopic description on a dynamical basis. It is shown that under very general assumptions concerning the nature of the system and the properties of the basic structural elements of the theory (under which subdynamics and synchronization need not hold in the generally adopted sense) the dynamical description goes over on the coarse-grained time scale into a closed, causal macrodescription with exponentially small error.