  We address the question of whether transport coefficients obtained from a
unitary closed system setting, i.e., the standard equilibrium Green-Kubo
formula, are the same as the ones obtained from a weakly driven nonequilibrium
steady-state calculation. We first derive a nonequilibrium Kubo-like expression
for the steady-state diffusion constant expressed as a time-integral of either
a current or a conserved density nonequilibrium correlation function. This
expression has certain advantages over the equilibrium Green-Kubo formula, but
is not clear if it gives the same value of the diffusion constant. We then
rigorously show that, if the unitary dynamics is diffusive the nonequilibrium
formula indeed gives exactly the same transport coefficient. The form of
finite-size correction is also predicted. Theoretical results are verified by
an explicit calculation of the diffusion constant in several interacting
many-body models.
