Adaptive Stochastic Methods for Sampling Driven Systems

Thermostatting methods are discussed in the context of canonical sampling in the presence of driving stochastic forces. Generalisations of the Nosé-Hoover method and Langevin dynamics are introduced which are able to dissipate excess heat introduced by steady Brownian perturbation (without a priori knowledge of its strength) while preserving ergodicity. Implementation and parameter selection are considered. It is demonstrated using numerical experiments that the methods derived can adaptively control the target canonical ensemble in the presence of nonlinear driving perturbations.