# Singly-Thermostated Ergodicity in Gibbs' Canonical Ensemble and the 2016 Ian Snook Prize Award

## TL;DR

This paper confirms the effectiveness of a new hyperbolic tangent thermostat in achieving ergodicity for various one-dimensional systems, advancing the development of single-thermostat algorithms for Gibbs' canonical ensemble.

## Contribution

It introduces a stiff hyperbolic tangent thermostat force and demonstrates its ability to produce Gibbs' distribution in several systems, addressing the challenge of ergodic algorithms with a single thermostat.

## Key findings

- Successfully reproduces Gibbs' distribution for multiple systems
- Confirms the ergodic properties of the new thermostat
- Highlights an interesting feature with adaptive integrators in the Mexican Hat problem

## Abstract

The 2016 Snook Prize has been awarded to Diego Tapias, Alessandro Bravetti, and David Sanders for their paper -- Ergodicity of One-Dimensional Systems Coupled to the Logistic Thermostat. They introduced a relatively stiff hyperbolic tangent thermostat force and successfully tested its ability to reproduce Gibbs' canonical distribution for the harmonic oscillator, the quartic oscillator, and the Mexican Hat potentials. Their work constitutes an effective response to the 2016 Ian Snook Prize Award goal -- Finding ergodic algorithms for Gibbs' canonical ensemble using a single thermostat variable. We confirm their work here and highlight an interesting feature of the Mexican Hat problem when it is solved with an adaptive integrator.