The Schweitz virial relation and how to compute the local pressure in molecular simulations

It is often assumed that computing the pressure is a routine operation in molecular dynamics simulations -- but this is not the case when the pressure varies across the simulation box. In this case special techniques are needed to compute the local pressure on lengthscales that may be comparable to the size of the molecules. I will show how this can be done. First I will show how the pressure is related to the "well known" Clausius virial relation for closed systems. Then I will generalise this relation to open systems and use this to derive two different, but equivalent, means for measuring the local pressure in molecular dynamics simulations.