  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. Existing dynamical studies showed
the absence of energy equipartitioning in such systems, hence their long-term
dynamics was described as quasi-equilibrium. Here we show that these systems do
in fact reach thermal equilibrium at sufficiently long times, as indicated by
the calculated heat capacity. This phase is described by equilibrium
statistical mechanics, opening up the possibility that the machinery of
non-equilibrium statistical mechanics may be used to understand the behaviour
of these systems away from equilibrium.
