The equilibrium phase in heterogeneous Hertzian chains

TL;DR

This paper studies how heterogeneous chains of macroscopic grains interacting via Hertz potential reach thermal equilibrium over time, analyzing the transition process and the role of correlations.

Contribution

It extends previous work by demonstrating that heterogeneous Hertzian chains also attain thermal equilibrium and introduces correlation functions to analyze the transition.

Findings

Heterogeneous chains reach thermal equilibrium at long times.

Heat capacity indicates the system's equilibrium state.

Correlation functions reveal the transition dynamics.

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. We previously showed that in homogeneous configurations of such systems, energy is equipartitioned at sufficiently long times, thus these systems ultimately reach thermal equilibrium. Here we expand on our previous work to show that heterogeneous configurations of grains also reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. We investigate the transition to equilibrium in detail and introduce correlation functions that indicate the onset of the transition.