Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid |
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Authors: | Attard Phil |
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Affiliation: | School of Chemistry F11, University of Sydney, New South Wales, Australia. attard@chem.usyd.edu.au |
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Abstract: | 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 Green-Kubo 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 Green-Kubo 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. |
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