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A Hamiltonian Formulation for Recursive Multiple Thermostats in a Common Timescale

2005; Society for Industrial and Applied Mathematics; Volume: 4; Issue: 1 Linguagem: Inglês

10.1137/040606090

1536-0040

Benedict Leimkuhler, Christopher Sweet,

Protein Structure and Dynamics

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.