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Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid

Summary: Statistical mechanical theory for steady-state systems.
III. Heat flow in a Lennard-Jones 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 short-time 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 steady-state probability distribution for heat
flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is
found to be accurate in the high-density 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
A theory for the structure, and dynamics of steady-state
systems was developed in Papers I and II of this series.1,2
The first paper gave explicit results for the structure of a
Lennard-Jones fluid that develops when a temperature gradi-


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


Collections: Chemistry