A gentle stochastic thermostat for molecular dynamics

We present a dynamical technique for sampling the canonical measure in molecular dynamics. The method 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, our method 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 the new dynamics generates the canonical distribution. In spite of its stochastic nature, it appears to have a relatively weak effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is tightly controlled even in the early stages of a simulation. Ben Leimkuhler · Emad Noorizadeh The Maxwell Institute and School of Mathematics, University of Edinburgh, EH9 3JZ, UK Florian Theil Mathematics Institute, University of Warwick, CV4 7AL, UK 2