Generalized Metropolis acceptance criterion for hybrid non-equilibrium molecular dynamics-Monte Carlo simulations

A family of hybrid simulation methods that combines the advantages of Monte Carlo (MC) with the strengths of classical molecular dynamics (MD) consists in carrying out short non-equilibrium MD (neMD) trajectories to generate new configurations that are subsequently accepted or rejected via an MC process. In the simplest case where a deterministic dynamic propagator is used to generate the neMD trajectories, the familiar Metropolis acceptance criterion based on the change in the total energy ΔE, min[1, exp{-βΔE}], guarantees that the hybrid algorithm will yield the equilibrium Boltzmann distribution. However, the functional form of the acceptance probability is more complex when the non-equilibrium switching process is generated via a non-deterministic stochastic dissipative propagator coupled to a heat bath. Here, we clarify the conditions under which the Metropolis criterion remains valid to rigorously yield a proper equilibrium Boltzmann distribution within hybrid neMD-MC algorithm.