 
Summary: Statistical mechanical theory for steady state systems. IV. Transition
probability and simulation algorithm demonstrated for heat flow
Phil Attarda
School of Chemistry F11, University of Sydney, NSW 2006 Australia
Received 11 October 2005; accepted 16 November 2005; published online 12 January 2006
Two microscopic transition theorems are given for the probability of nonequilibrium work
performed on a subsystem of a thermal reservoir along the trajectory in phase space of the
subsystem. The resultant transition probability is applied to the case of heat flow down an applied
temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such
a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement
with previous GreenKubo and nonequilibrium molecular dynamics results. © 2006 American
Institute of Physics. DOI: 10.1063/1.2151887
I. INTRODUCTION
Computer simulations at the molecular level have been
used to describe the properties of a wide variety of equilib
rium systems.1
In contrast the timedependent processes of
nonequilibrium systems pose special challenges to obtaining
properties such as transport coefficients or rates of reaction,
nucleation, or transformation, etc. Unlike the equilibrium
