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Abstract
A realization of the projection operators is proposed which makes it possible to apply the master equations as written by Zwanzig to the general case of a finite non-uniform system. The main characteristics of the method are: the realization is defined for a reduced description, the projectors do not operate in Hilbert space but provide a partition of the terms of a perturbation expansion; the approach is deductive, the realization deriving from the structure of the system Hamiltonian.