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

Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results