Journal of Statistical Physics

, Volume 135, Issue 2, pp 261–277

A Gentle Stochastic Thermostat for Molecular Dynamics


DOI: 10.1007/s10955-009-9734-0

Cite this article as:
Leimkuhler, B., Noorizadeh, E. & Theil, F. J Stat Phys (2009) 135: 261. doi:10.1007/s10955-009-9734-0


We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.


Ergodicity Hypoellipticity Temperature control Molecular dynamics Nosé-Hoover thermostat 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Ben Leimkuhler
    • 1
  • Emad Noorizadeh
    • 1
  • Florian Theil
    • 2
  1. 1.The Maxwell Institute and School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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