The thermal conductance of nanoscale phonon modes is typically calculated using the Boltzmann transport equation. A particular implementation of this method is the acoustic mismatch model (AMM) that compares impedance ratios at a mathematically abrupt transition between two equilibrium regions. The shortcomings of this model can be rectified by starting from a microscopic physics based equation describing the propagation of phonon waves across an extended junction, with carefully computed thermal boundary conditions on either side. The resulting nonequilibrium Green’s function (NEGF) formalism provides an accurate yet physically transparent machinery to calculate energy transfer, especially in nanosystems where the concept of thermal equilibrium breaks down readily. The purpose of this paper is to establish the NEGF formalism of thermal conductivity with a few simple examples and illustrate its particular strengths compared to the AMM.

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