  We study the molecular dynamics of two discs undergoing Newtonian
("inertial") dynamics, with elastic collisions in a rectangular box. Using a
mapping to a billiard model and a key result from ergodic theory, we obtain
exact, analytical expressions for the mean times between the following events:
hops, i.e.~horizontal or vertical interchanges of the particles; wall
collisions; and disc collisions. To do so, we calculate volumes and
cross-sectional areas in the four-dimensional configuration space. We compare
the analytical results against Monte Carlo and molecular dynamics simulations,
with excellent agreement.
