  The recently introduced multisite tensor network path integral (MS-TNPI)
method [Bose and Walters, J. Chem. Phys., 2022, 156, 24101.] for simulation of
quantum dynamics of extended systems has been shown to be effective in studying
one-dimensional systems. Quantum transport in these systems are typically
studied at a constant temperature. However, temperature seems to be a very
obvious parameter that can be spatially changed to control the quantum
transport. Here, MS-TNPI is used to study ``non-equilibrium'' effects of an
externally imposed temperature gradient on the quantum transport in
one-dimensional extended quantum systems.
