  In a recent publication [W. Dou, G. Miao, and J. E. Subotnik, Phys. Rev.
Lett. 119, 046001 (2017)], using the quantum-classical Liouville equation
(QCLE), we derived a very general form for the electronic friction felt by a
molecule moving near one or many metal surfaces. Moreover, we have already
proved the equivalence of the QCLE electronic friction with the
Head-Gordon--Tully model as well as a generalized version of von Oppen's
nonequilibrium Green's function (NEGF) method at equilibrium [W. Dou and J. E.
Subotnik, Phys. Rev. B 96, 104305 (2017)]. In the present paper, we now further
prove the equivalence between the QCLE friction and the NEGF friction for the
case of multiple metal surfaces and an out-of-equilibrium electronic current.
The present results conclude our recent claim that there is only one universal
electronic friction tensor arising from the Born-Oppenheimer approximation.
