Slow relaxation to equipartition in spring-chain systems

TL;DR

This paper investigates how spring-chain systems of masses connected by springs relax to thermal equilibrium, revealing that end particles initially have higher kinetic energy and that the relaxation timescale depends on spring stiffness.

Contribution

It demonstrates the transient nature of end particle energy excess in spring-chain systems and connects relaxation timescales with spring constants using Boltzmann-Jeans theory.

Findings

End particles have higher initial kinetic energy than others.

Relaxation to equipartition occurs over a timescale increasing with spring constant.

Boltzmann-Jeans theory accurately estimates relaxation timescale.

Abstract

In this study, one-dimensional systems of masses connected by springs, i.e., spring-chain systems, are investigated numerically. The average kinetic energy of chain-end particles of these systems is larger than that of other particles, which is similar to the behavior observed for systems made of masses connected by rigid links. The energetic motion of the end particles is, however, transient, and the system relaxes to thermal equilibrium after a while, where the average kinetic energy of each particle is the same, that is, equipartition of energy is achieved. This is in contrast to the case of systems made of masses connected by rigid links, where the energetic motion of the end particles is observed in equilibrium. The timescale of relaxation estimated by simulation increases rapidly with increasing spring constant. The timescale is also estimated using the Boltzmann-Jeans theory and is found to be in quite good agreement with that obtained by the simulation.