  We examine the long-term behaviour of non-integrable, energy-conserved, 1D
systems of macroscopic grains interacting via a contact-only generalized Hertz
potential and held between stationary walls. We previously showed that in
homogeneous configurations of such systems, energy is equipartitioned at
sufficiently long times, thus these systems ultimately reach thermal
equilibrium. Here we expand on our previous work to show that heterogeneous
configurations of grains also reach thermal equilibrium at sufficiently long
times, as indicated by the calculated heat capacity. We investigate the
transition to equilibrium in detail and introduce correlation functions that
indicate the onset of the transition.
