  Since crystals are made of periodic structures in space, predicting their
three period vectors starting from any values based on the inside interactions
is a basic theoretical physics problem. For the general situation where
crystals are under constant external stress, we derived dynamical equations of
the period vectors in the framework of Newtonian dynamics, for pair potentials
recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show
that the period vectors are driven by the imbalance between the internal and
external stresses. This presents a physical process where when the external
stress changes, the crystal structure changes accordingly, since the original
internal stress can not balance the external stress. The internal stress has
both a full kinetic energy term and a full interaction term. It is extended to
many-body interactions in this paper. As a result, all conclusions in the
pair-potential case also apply for many-body potentials.
