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We derive expressions of interatomic force and heat current for many-bodypotentials such as the Tersoff, the Brenner, and the Stillinger-Weber potentialused extensively in molecular dynamics simulations of covalently bondedmaterials. Although these potentials have a many-body nature, a pairwise forceexpression that follows Newton's third law can be found without referring toany partition of the potential. Based on this force formula, a stressapplicable for periodic systems can be unambiguously defined. The force formulacan then be used to derive the heat current formulas using a natural potentialpartitioning. Our heat current formulation is found to be equivalent to most ofthe seemingly different heat current formulas used in the literature, but todeviate from the stress-based formula derived from two-body potential. Wevalidate our formulation numerically on various systems descried by the Tersoffpotential, namely three-dimensional silicon and diamond, two-dimensionalgraphene, and quasi-one-dimensional carbon nanotube. The effects of cell sizeand time used in the simulation are examined.

Force and heat current formulas for many-body potentials in molecular dynamics simulation with applications to thermal conductivity calculations