This work examines existing formalisms for the derivation of microscopic momentum and heat fluxes. Both analytical and simulation results are provided to show that the widely used flux formulas are not applicable to transient transport processes or highly inhomogeneous systems, e.g., materials with atomically sharp interfaces. A method is formulated for formally deriving microscopic momentum and heat fluxes through the integral representation of conservation laws. The resulting flux formulas are mathematically rigorous, fully consistent with the physical concepts of momentum and heat fluxes, and applicable to nonequilibrium transient processes in atomically inhomogeneous systems with general many-body forces.

• Received 1 August 2016
• Revised 27 October 2016

DOI:https://doi.org/10.1103/PhysRevE.94.053309