  We clarify some misunderstandings on the time-dependent current density
functional theory for open quantum systems we have recently introduced [M. Di
Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show
that some of the recent formulations attempting to improve on this theory
suffer from some inconsistencies, especially in establishing the mapping
between the external potential and the quantities of interest. We offer a
general argument about this mapping, showing that it must fulfill certain
"dimensionality" requirements.
