The properties of systems composed of atoms interacting though discrete potentials are
dictated by a series of events which occur between pairs of atoms. There are only four basic
event types for pairwise discrete potentials and the square-well/shoulder systems studied
here exhibit them all. Closed analytical expressions are derived for the on-event kinetic
energy distribution functions for an atom, which are distinct from the Maxwell–Boltzmann
distribution function. Exact expressions are derived that directly relate the pressure and …