Long-term behaviour of Hertzian chains between fixed walls is really equilibrium

Abstract

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.