 
Summary: Statistical mechanical theory for steadystate systems.
III. Heat flow in a LennardJones fluid
Phil Attarda
School of Chemistry F11, University of Sydney, New South Wales 2006 Australia
Received 15 March 2005; accepted 4 May 2005; published online 28 June 2005
A statistical mechanical theory for heat flow is developed based upon the second entropy for
dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained
from a GreenKubo integral of a time correlation function, is derived as an approximation from
these more fundamental theories, and its shorttime dependence is explored. A new expression for
the thermal conductivity is derived and shown to converge to its asymptotic value faster than the
traditional GreenKubo expression. An ansatz for the steadystate probability distribution for heat
flow down an imposed thermal gradient is tested with simulations of a LennardJones fluid. It is
found to be accurate in the highdensity regime at not too short times, but not more generally. The
probability distribution is implemented in Monte Carlo simulations, and a method for extracting the
thermal conductivity is given. © 2005 American Institute of Physics. DOI: 10.1063/1.1942491
I. INTRODUCTION
A theory for the structure, and dynamics of steadystate
systems was developed in Papers I and II of this series.1,2
The first paper gave explicit results for the structure of a
LennardJones fluid that develops when a temperature gradi
