Information theory applied to the transport coefficients of Lennard-Jones fluids

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Abstract
Expressions with no disposable parameters are derived for the self-diffusion coefficient D, shear viscosity, η and thermal conductivity κ of simple liquids in terms of the frequency-transform moments of the relevant time correlation function in the Green-Kubo formulae. We use information theory to derive analytic expressions for these transport coefficients. We also use a Mori-series expansion of the frequency transform of the time correlation function to obtain other estimates of the transport coefficients, including exponential, hyperbolicsecant and Gaussian memory functions, and also geometric-mean closures. Simulations are performed on Lennard-Jones fluid states to calculate both the appropriate frequency moments and also the transport coefficients directly during the same computation. Comparison of the various analytic expressions with the molecular-dynamics simulation values for the transport coefficients reveals that the best agreement is found with one of the analytic memoryfunction closures (the precise form depending on the region of the phase diagram and also on the order of the moment expansion considered). The geometric-mean and low-order information-theory expansions have the advantage, however, that they show fair agreement over the whole phase diagram.