  We study the problem of calculating transport properties of interacting
quantum systems, specifically electrical and thermal conductivities, by
computing the non-equilibrium steady state (NESS) of the system biased by
contacts. Our approach is based on the structure of entanglement in the NESS.
With reasonable physical assumptions, we show that a NESS close to local
equilibrium is lightly entangled and can be represented via a computationally
efficient tensor network. We further argue that the NESS may be found by
dynamically evolving the system within a manifold of appropriate low
entanglement states. A physically realistic law of dynamical evolution is
Markovian open system dynamics, or the Lindblad equation. We explore this
approach in a well-studied free fermion model where comparisons with the
literature are possible. We study both electrical and thermal currents with and
without disorder, and compute entropic quantities such as mutual information
and conditional mutual information. We conclude with a discussion of the
prospects of this approach for the challenging problem of transport in strongly
interacting systems, especially those with disorder.
