Density-Functional Theory of Thermal Transport

We have recently introduced a non-equilibrium density-functional theory of local temperature and associated energy density that is suitable for the study of thermoelectric phenomena from first principles [1]. This theory rests on a local temperature field coupled to the energy-density operator. Here we apply the theory to a simple two-terminal setup, in which the terminals are held at different temperatures. We show that our treatment becomes equivalent to the standard Landauer-B{\"u}ttiker formulation of thermal transport in the non-interacting limit. \\[4pt] [1] arXiv:1308.2311