  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. As a byproduct, we show how fluctuations of
system quantities, and thus the distribution functions, are influenced by the
Hertz potential. In particular, the variance of the system's kinetic energy
probability density function is reduced by a factor related to the contact
potential.
