“…However, at the nanometer scale, such approaches are no more valid and must be replaced by models treating thermal transport at the phonon level. Nowadays, most theoretical investigations of nanoscale thermal transport are based either (i) on the linearized Boltzmann Transport Equation with Fermi's Golden Rule 15,16,20,21 , (phonon quantum confinement neglected) (ii) on Equilibrium Molecular Dynamics simulations 23 (computationally very intensive and statistical average over long time periods required), (iii) on first-principle (ab-initio) methods 19 (limited to very small systems), or (iv) on coherent phonon Non-equilibrium Green's Function (NEGF) approaches 12,17,22 (no dissipative interactions). The versatility and flexibility of NEGF 25,26 make it one of the most widely-spread and appreciated formalisms to solve quantum transport problems.…”