Statistical mechanical theory for non-equilibrium systems. IX. Stochastic molecular dynamics

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin's friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic equations of motion. Setting the variance to zero but keeping the friction coefficient nonzero reduces the theory to a Hoover thermostat without explicit constraint, although such a limit violates the physical requirement of proportionality between the dissipation and the fluctuation. A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle.