  We investigate the Lindblad equation in the context of boundary-driven
magnetization transport in spin-$1/2$ chains. Our central question is whether
the nonequilibrium steady state of the open system, including its buildup in
time, can be described on the basis of the dynamics in the closed system. To
this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where
a description in terms of spatio-temporal correlation functions has been
suggested in the case of weak driving and small system-bath coupling. Because
this work has focused on integrable systems and periodic boundary conditions,
we here extend the analysis in three directions: We (i) consider nonintegrable
systems, (ii) take into account open boundary conditions and other
bath-coupling geometries, and (iii) provide a comparison to time-evolving block
decimation. While we find that nonintegrability plays a minor role, the choice
of the specific boundary conditions can be crucial, due to potentially
nondecaying edge modes. Our large-scale numerical simulations suggest that a
description based on closed-system correlation functions is an useful
alternative to already existing state-of-the-art approaches.
