  Quantum simulation methods based on density-functional theory are currently
deemed unfit to cope with atomic heat transport within the Green-Kubo
formalism, because quantum-mechanical energy densities and currents are
inherently ill-defined at the atomic scale. We show that, while this difficulty
would also affect classical simulations, thermal conductivity is indeed
insensitive to such ill-definedness by virtue of a sort of gauge invariance
resulting from energy extensivity and conservation. Based on these findings, we
derive an expression for the adiabatic energy flux from density-functional
theory, which allows heat transport to be simulated using ab-initio equilibrium
molecular dynamics. Our methodology is demonstrated by comparing its
predictions with those of classical equilibrium and ab-initio non-equilibrium
(M\"uller-Plathe) simulations for a liquid-Argon model, and finally applied to
heavy water at ambient conditions.
