Transport in nanoscale systems: the microcanonical versus grand-canonical picture

We analyse a picture of transport in which two large but finite charged electrodes discharge across a nanoscale junction. We identify a functional whose minimisation, within the space of all bound many-body wavefunctions, defines an instantaneous steady state. We also discuss factors that favour the onset of steady-state conduction in such systems, make a connection with the notion of entropy, and suggest a novel source of steady-state noise. Finally, we prove that the true many-body total current in this closed system is given exactly by the one-electron total current, obtained from time-dependent density-functional theory.