Calculation of Microscopic Stress Tensor with Non-equilibrium Molecular Dynamics

Abstract

We define local momentum density as the vector field of momentum using Dirac’s delta functions. The local momentum density should satisfy the continuity equation with a tensor field and then this tensor field is regarded as local momentum flux composed of advective term and stress tensor. From this theory, when the target region is selected arbitrarily, the stress tensor and pressure tensor on the target region can be calculated by particle simulations such as molecular dynamics simulation. Because the distribution function is not required by this theory, the stress tensor can be calculated in the non-equilibrium molecular dynamics.