Generating generalized distributions from dynamical simulation

TL;DR: In this article, a general molecular-dynamics simulation scheme, based on the Nose thermostat, for sampling from arbitrary phase space distributions is presented, and numerical methods based on both Nose-Hoover and Nose-Poincare thermostats for two specific classes of distributions are formulated.

Abstract: We present a general molecular-dynamics simulation scheme, based on the Nose thermostat, for sampling from arbitrary phase space distributions. We formulate numerical methods based on both Nose–Hoover and Nose–Poincare 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.