Local stress and heat flux in atomistic systems involving three-body forces

Local densities of fundamental physical quantities, including stress and heat flux fields, are formulated for atomistic systems involving three-body forces. The obtained formulas are calculable within an atomistic simulation, in consistent with the conservation equations of thermodynamics of continuum, and can be applied to systems with general two- and three-body interaction forces. It is hoped that this work may correct some misuse of inappropriate formulas of stress and heat flux in the literature, may clarify the definition of site energy of many-body potentials, and may serve as an analytical link between an atomistic model and a continuum theory. Physical meanings of the obtained formulas, their relation with virial theorem and heat theorem, and the applicability are discussed.