Conservation laws at nano/micro scales

This paper aims to find a field description of local conservation laws at nano/ micro scales. Atomistic definitions and field representations of fundamental physical quantities are presented. By decomposing atomic deformation into homogeneous lattice deformation and inhomogeneous relative atomic deformation, and also decomposing momentum flux and heat flux into homogeneous and inhomogeneous parts, the field representations of conservation laws at atomic scale have been formulated, which follow exactly the time evolution laws that exist in atomistic simulations, where the atomic motion is fully described, the inhomogeneous internal motion is not ignored, and the smallest particles considered are atoms.