Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods

Ben Leimkuhler, Emad Noorizadeh, Oliver Penrose

Research output: Contribution to journalArticle

Abstract

Molecular dynamics typically incorporates a stochastic-dynamical device, a "thermostat," in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the "efficiency" of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321-1336, 2007) and a generalization of the "stochastic velocity rescaling" method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates. © 2011 Springer Science+Business Media, LLC.

Original languageEnglish
Pages (from-to)921-942
Number of pages22
JournalJournal of Statistical Physics
Volume143
Issue number5
DOIs
Publication statusPublished - Jun 2011

Fingerprint

thermostats
molecular dynamics
estimates
autocorrelation
degrees of freedom
kinetic energy
perturbation
temperature

Keywords

  • Langevin dynamics
  • Molecular dynamics
  • Nosé-Hoover
  • Stochastic thermostats
  • Stochastic velocity rescaling
  • Thermodynamic averages

Cite this

Leimkuhler, Ben ; Noorizadeh, Emad ; Penrose, Oliver. / Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods. In: Journal of Statistical Physics. 2011 ; Vol. 143, No. 5. pp. 921-942.
@article{44755b94bb5f4c838ae3173bdd309539,
title = "Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods",
abstract = "Molecular dynamics typically incorporates a stochastic-dynamical device, a {"}thermostat,{"} in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the {"}efficiency{"} of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nos{\'e}-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321-1336, 2007) and a generalization of the {"}stochastic velocity rescaling{"} method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates. {\circledC} 2011 Springer Science+Business Media, LLC.",
keywords = "Langevin dynamics, Molecular dynamics, Nos{\'e}-Hoover, Stochastic thermostats, Stochastic velocity rescaling, Thermodynamic averages",
author = "Ben Leimkuhler and Emad Noorizadeh and Oliver Penrose",
year = "2011",
month = "6",
doi = "10.1007/s10955-011-0210-2",
language = "English",
volume = "143",
pages = "921--942",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer",
number = "5",

}

Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods. / Leimkuhler, Ben; Noorizadeh, Emad; Penrose, Oliver.

In: Journal of Statistical Physics, Vol. 143, No. 5, 06.2011, p. 921-942.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods

AU - Leimkuhler, Ben

AU - Noorizadeh, Emad

AU - Penrose, Oliver

PY - 2011/6

Y1 - 2011/6

N2 - Molecular dynamics typically incorporates a stochastic-dynamical device, a "thermostat," in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the "efficiency" of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321-1336, 2007) and a generalization of the "stochastic velocity rescaling" method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates. © 2011 Springer Science+Business Media, LLC.

AB - Molecular dynamics typically incorporates a stochastic-dynamical device, a "thermostat," in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the "efficiency" of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321-1336, 2007) and a generalization of the "stochastic velocity rescaling" method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates. © 2011 Springer Science+Business Media, LLC.

KW - Langevin dynamics

KW - Molecular dynamics

KW - Nosé-Hoover

KW - Stochastic thermostats

KW - Stochastic velocity rescaling

KW - Thermodynamic averages

U2 - 10.1007/s10955-011-0210-2

DO - 10.1007/s10955-011-0210-2

M3 - Article

VL - 143

SP - 921

EP - 942

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 5

ER -