The Andersen thermostat in molecular dynamics

We carry out a mathematical study of the Andersen thermostat [1], which is a frequently used tool in molecular dynamics. After reformulating the continuous-and discrete-time Andersen dynamics, we prove that in both cases the Andersen dynamics is uniformly ergodic. A detailed numerical analysis is presented, establishing the rate of convergence of most commonly used numerical algorithms for the Andersen thermostat. Transport properties such as the diffusion constant are also investigated. It is proved for the Lorentz gas model where there is intrinsic diffusion that the diffusion coefficient calculated using the Andersen thermostat converges to the true diffusion coefficient in the limit of vanishing collision frequency in the Andersen thermostat.