Is the microscopic stress computed from molecular simulations in mechanical equilibrium?

The microscopic stress field provides a unique connection between molecular simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of atomistic and coarse-grained systems with multi-body potentials. We explore the local stress of systems including lipid membranes, fibrous proteins, and defective graphene. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium. We present an unambiguous and physically sound geometric definition of the microscopic stress based on a covariance argument. Our approach provides objective expressions to compute microscopic stress fields satisfying balance of linear and angular momentum, for force-fields with arbitrarily high many-body interactions.