Atomistic formulas for local properties in systems with many-body interactions.

Atomistic formulas are derived for the local densities and fluxes used in the continuum description of energy and momentum transport. Two general methods for the distribution of potential energy among a system's constituent particles are presented and analyzed. The resulting formulas for the heat flux and stress tensor and the equations for energy and momentum transport are exact consequences of the definitions of the densities and the equations of classical mechanics. The formulas and equations obtained are valid for systems with very general types of many-body interactions.