 
Summary: Statistical mechanical theory for nonequilibrium systems. IX.
Stochastic molecular dynamics
Phil Attarda
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 13 February 2009; accepted 28 April 2009; published online 20 May 2009
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 fluctuationdissipation 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 timevarying, driven Brownian particle. © 2009
American Institute of Physics. DOI: 10.1063/1.3138762
I. INTRODUCTION
Computer simulations are in principle exact and they
provide reliable, quantitative data for realistic models, as
well as benchmark results to test approximate theories. The
two main equilibrium simulation techniques are Monte Carlo
