On the derivation of some fundamental expressions for the average stress tensor in systems of interacting particles

The so-called generalized Kramers-Kirkwood expression for the average stress tensor of a system of interacting point particles, derived by Bird and Curtiss on using a phase-space-kinetic formalism has been reconsidered from different points of view. First a derivation based upon volume averaging is discussed, and after that a derivation based upon a virtual work principle. The latter approach offers the possibility of distinguishing reversible (including thermodynamic and Brownian) and dissipative forces and stresses by using a projection operator, associated with the constraints of the system.