Abstract
We introduce simple diagrams and rules to calculate the exact time-local master equation for an arbitrary open quantum system interacting with a bath. In it, the time-convolutionless generator is expanded in the system-bath coupling to all orders, and the $n\mathrm{th}$-order contribution is expressed by the superoperators generated from the system operator in the system-bath coupling and the associated $n$-point nonequilibrium correlation functions of the environment operators. This theory generalizes previous attempts to obtain the time-convolutionless generator and provides a general framework to study the non-Markovian, nonequilibrium dynamics of open quantum systems.
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