Newtonian mechanics of a many-particle assembly coupled to an external body potential

The Newtonian mechanics of a many-particle system evolving in time under the influence of an external body potential, that is, an external potential that couples to the center of mass only, is examined. The lack of any other external fields allows the complete separation of the center-of-mass (or external-field-dependent) equations from the internal (or external-field-independent) dynamics. The complete solution of the center-of-mass motion then allows an analytical evaluation of the external body potential contributions to the thermophysical properties of the system. The phenomena of field-induced heating, Taylor-Aris hydrodynamic form for the diffusion tensor, and an analogous hydrodynamic form for the viscosity tensor are derived from microscopic principles. A brief and model-dependent description of equilibrium phenomena is also presented.