Ergodicity of the Nos\'e-Hoover method

TL;DR

This paper investigates the ergodic properties of systems using the Nosé-Hoover thermostat, revealing conditions under which the system loses or gains ergodicity due to the dynamics of heatbath variables.

Contribution

It provides a detailed analysis of the heatbath variables' dynamics, showing how periodicity leads to non-ergodicity and chaos induces ergodicity in these systems.

Findings

Heatbath variables can be periodic, causing non-ergodicity.

Chaotic heatbath variables lead to ergodic behavior.

Periodic behavior correlates with loss of ergodicity.

Abstract

Ergodicity of the systems with Nos\'e-Hoover thermostat are studied. The dynamics of the heatbath variables are investigated and they can be periodic when the system has quick oscillation. The periodic behaviour of them causes the system to lose its ergodicity. The kinetic-moments method is also studied, and the heatbath variables in this method are found to be chaotic. The chaotic behaviour makes the whole system ergodic.