  A two-step unified framework for the evaluation of continuum field
expressions from molecular simulations for arbitrary interatomic potentials is
presented. First, pointwise continuum fields are obtained using a
generalization of the Irving-Kirkwood procedure to arbitrary multi-body
potentials. Two ambiguities associated with the original Irving-Kirkwood
procedure (which was limited to pair potential interactions) are addressed in
its generalization. The first ambiguity is due to the non-uniqueness of the
decomposition of the force on an atom as a sum of central forces, which is a
result of the non-uniqueness of the potential energy representation in terms of
distances between the particles. This is in turn related to the shape space of
the system. The second ambiguity is due to the non-uniqueness of the energy
decomposition between particles. The latter can be completely avoided through
an alternate derivation for the energy balance. It is found that the
expressions for the specific internal energy and the heat flux obtained through
the alternate derivation are quite different from the original Irving-Kirkwood
procedure and appear to be more physically reasonable. Next, in the second step
of the unified framework, spatial averaging is applied to the pointwise field
to obtain the corresponding macroscopic quantities. These lead to expressions
suitable for computation in molecular dynamics simulations. It is shown that
the important commonly-used microscopic definitions for the stress tensor and
heat flux vector are recovered in this process as special cases (generalized to
arbitrary multi-body potentials). Several numerical experiments are conducted
to compare the new expression for the specific internal energy with the
original one.
