A hamiltonian formulation for recursive multiple thermostats in a common timescale

Benedict J. Leimkuhler*, Christopher R. Sweet

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Molecular dynamics trajectories that sample from a Gibbs distribution can be generated by introducing a modified Hamiltonian with additional degrees of freedom as described by Nosé [S. Nosé, Mol. Phys., 52 (1984), p. 255]. To achieve the ergodicity required for canonical sampling, a number of techniques have been proposed based on incorporating additional thermostatting variables, such as Nosé-Hoover chains and more recent fully Hamiltonian generalizations. For Nosé dynamics, it is often stated that the system is driven to equilibrium through a resonant interaction between the self-oscillation frequency of the thermostat variable and a natural frequency of the underlying system. In this article, we clarify this perspective, using harmonic models, and exhibit practical deficiencies of the standard Nosé chain approach. As a consequence of our analysis, we propose a new powerful "recursive thermostatting" procedure which obtains canonical sampling without the stability problems encountered with Nosé-Hoover and Nosé-Poincaré chains.

Original languageEnglish
Pages (from-to)187-216
Number of pages30
JournalSiam Journal on Applied Dynamical Systems
Issue number1
Publication statusPublished - 2005

Keywords / Materials (for Non-textual outputs)

  • Constant temperature molecular dynamics
  • Nosé
  • Nosé-Hoover
  • Nosé-Poincaré
  • Nosé-Poincaré chains
  • Symplectic integrator
  • Thermostatting


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