Master equations are increasingly popular for the simulation oftime-dependent electronic transport in nanoscale devices. Several recentMarkovian approaches use "extended reservoirs" - explicit degrees of freedomassociated with the electrodes - distinguishing them from many previous classesof master equations. Starting from a Lindblad equation, we develop a commonfoundation for these approaches. Due to the incorporation of explicit electrodestates, these methods do not require a large bias or even "true Markovianity"of the reservoirs. Nonetheless, their predictions are only physically relevantwhen the Markovian relaxation is weaker than the thermal broadening and whenthe extended reservoirs are "sufficiently large," in a sense that we quantify.These considerations hold despite complete positivity and respect for Pauliexclusion at any relaxation strength.
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