 
Summary: Statistical mechanical theory for the structure of steady state systems:
Application to a LennardJones fluid with applied temperature gradient
Phil Attard
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 21 June 2004; accepted 21 July 2004
The constrained entropy and probability distribution are given for the structure that develops in
response to an applied thermodynamic gradient, as occurs in driven steady state systems. The theory
is linear but is applicable to gradients with arbitrary spatial variation. The phase space probability
distribution is also given, and it is surprisingly simple with a straightforward physical interpretation.
With it, all of the known methods of equilibrium statistical mechanics for inhomogeneous systems
may now be applied to determining the structure of nonequilibrium steady state systems. The theory
is illustrated by performing Monte Carlo simulations on a LennardJones fluid with externally
imposed temperature and chemical potential gradients. The induced energy and density moments are
obtained, as well as the moment susceptibilities that give the rate of change of these with imposed
gradient and which also give the fluctuations in the moments. It is shown that these moment
susceptibilities can be written in terms of bulk susceptibilities and also that the Soret coefficient can
be expressed in terms of them. © 2004 American Institute of Physics. DOI: 10.1063/1.1792573
I. INTRODUCTION
There are two distinct aspects to a driven, nonequilib
rium, steady state system: the structure and the flux. For
