Fluctuations in Hertz chains at equilibrium

TL;DR

This study demonstrates that 1D Hertz chain systems, previously thought to be quasi-equilibrium, actually reach thermal equilibrium over long times, with fluctuations influenced by the contact potential.

Contribution

It provides evidence that Hertz chains attain thermal equilibrium at long times and analyzes how the Hertz potential affects fluctuations and distribution functions.

Findings

Hertz chains reach thermal equilibrium at long times.

Fluctuations are affected by the Hertz potential.

Variance of kinetic energy distribution is reduced.

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. 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.