  We have previously shown an analysis of our dimer model in the over-damped
regime to show directed transport in equilibrium. Here we analyze the full
model with inertial terms present to establish the same result. First we derive
the Fokker-Planck equation for the system following a Galilean transformation
to show that a uniformly translating equilibrium distribution is possible.
Then, we find out the velocity selection for the centre of mass motion using
that distribution on our model. We suggest generalization of our calculations
for soft collision potentials and indicate to interesting situation with
possibility of oscillatory non-equilibrium state within equilibrium.
