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In this paper, we develop a consistent perturbative technique for obtaining atime-local master equation based on projective methods in the case where theprojector depends on time. We then introduce a generalization of theKawasaki--Gunton projector, which allows us to use this technique to derive,generally speaking, nonlinear master equations in the case of arbitraryansatzes consistent with some set of observables. Most of our results are verygeneral, but in our discussion we focus on the application of these results tothe theory of open quantum systems.

On time-dependent projectors and on generalization of thermodynamical approach to open quantum systems