Statistical mechanical theory for the structure of steady state systems: application to a Lennard-Jones fluid with applied temperature gradient.

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 Lennard-Jones 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.