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The time-convolutionless master equation provides a general framework tomodel non-Markovian dynamics of an open quantum system with a time-localgenerator. A diagrammatic representation is developed and proven for theperturbative expansion of the exact time-local generator for an open quantumsystem interacting with arbitrary environments. A truncation of theperturbation expansion leads to the perturbative time-convolutionless quantummaster equations. We further introduce a nonperturbative approach thatapproximates the time-convolutionless generator as a nested time-orderedexponential function.

Diagrammatic representation and nonperturbative approximation of exact time-convolutionless master equation