E. Barth, B. Laird, B. Leimkuhler

We present a general molecular-dynamics simulation scheme, based on the Nos\'e thermostat, for sampling according to arbitrary phase space distributions. We formulate numerical methods based on both Nos\'{e}-Hoover and Nos\'{e}-Poincar\'{e} thermostats for two specific classes of distributions; namely, those that are functions of the system Hamiltonian and those for which position and momentum are statistically independent. As an example, we propose a generalized variable temperature distribution that is designed to accelerate sampling in molecular systems.