Non-equilibrium Green's function formalism for radiative heat transfer

Abstract Radiative heat transfer (RHT) at the nanoscale can vastly exceed the far-field blackbody limit due to the tunneling of evanescent waves, a phenomenon traditionally described by fluctuational electrodynamics (FE). While FE has been exceptionally successful for systems in local thermal equilibrium, its foundational assumptions break down in the growing number of scenarios involving genuine non-equilibrium conditions, such as in active devices or driven materials. This review introduces the non-equilibrium Green's function (NEGF) formalism as a powerful and versatile framework to study RHT beyond these classical limits. Rooted in quantum many-body theory, NEGF provides a unified language to describe energy transport by photons, electrons, and phonons on an equal footing. We first outline the theoretical foundations of the NEGF approach for RHT, demonstrating how it recovers the canonical results of FE in the local equilibrium limit. We then survey recent breakthroughs enabled by NEGF, including: (i) providing a quantum-accurate description of equilibrium RHT that naturally incorporates non-local and finite-size effects, resolving unphysical divergences predicted by local models; (ii) unifying heat transfer channels to reveal the non-additive synergy between radiation, electron tunneling, and phonon conduction at sub-nanometer gaps; (iii) enabling the quantum design of materials and metamaterials with tailored thermal properties through band structure and topological engineering; and (iv) describing active control of heat flow in driven systems, which allows for phenomena like isothermal heat transfer and pumping heat against a temperature gradient. By shifting the paradigm from passive analysis to active control and design, the NEGF formalism opens a new frontier for manipulating thermal energy at the nanoscale, with profound implications for thermal management, energy conversion, and thermal information processing.