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

## TL;DR

This study demonstrates that non-integrable 1D Hertzian chains between fixed walls eventually reach thermal equilibrium, challenging previous notions of persistent quasi-equilibrium states and enabling the application of equilibrium statistical mechanics.

## Contribution

The paper provides evidence that such systems do attain true equilibrium at long times, which was previously thought unlikely, thus bridging non-equilibrium dynamics and equilibrium statistical mechanics.

## Key findings

- Systems reach thermal equilibrium indicated by heat capacity calculations.
- Long-term dynamics are consistent with equilibrium statistical mechanics.
- Challenges previous views of persistent quasi-equilibrium states.

## 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.