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Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density

Summary: Statistical mechanical theory for steady state systems.
V. Nonequilibrium probability density
Phil Attarda
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 15 March 2006; accepted 17 April 2006; published online 12 June 2006
The phase space probability density for steady heat flow is given. This generalizes the Boltzmann
distribution to a nonequilibrium system. The expression includes the nonequilibrium partition
function, which is a generating function for statistical averages and which can be related to a
nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the
linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the
probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown
to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the
Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the
generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent
mechanical work, and for nonequilibrium quantum statistical mechanics. 2006 American Institute
of Physics. DOI: 10.1063/1.2203069
This paper is the culmination of a series on the theory of
steady state systems.14
The goal of the research has been to


Source: Attard, Phil - School of Chemistry, University of Sydney


Collections: Chemistry