Heat conduction in nanoscale materials: A statistical-mechanics derivation of the local heat flux

We derive a coarse-grained model for heat conduction in nanoscale mechanical systems. Starting with an all-atom description, this approach yields a reduced model, in the form of conservation laws of momentum and energy. The model closure is accomplished by introducing a quasilocal thermodynamic equilibrium, followed by a linear response approximation. Of particular interest is the constitutive relation for the heat flux, which is expressed nonlocally in terms of the spatial and temporal variation of the temperature. Nanowires made of copper and silicon are presented as examples.