Journal of Statistical Physics

, Volume 143, Issue 5, pp 921–942

Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods


DOI: 10.1007/s10955-011-0210-2

Cite this article as:
Leimkuhler, B., Noorizadeh, E. & Penrose, O. J Stat Phys (2011) 143: 921. doi:10.1007/s10955-011-0210-2


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.


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

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ben Leimkuhler
    • 1
  • Emad Noorizadeh
    • 1
  • Oliver Penrose
    • 2
  1. 1.The Maxwell Institute and School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.The Maxwell Institute and Department of MathematicsHeriot-Watt UniversityEdinburghUK

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