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Spatially nonlocal fluctuation theories: Hydrodynamic fluctuations for simple fluids

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  • Keizer, Joel
  • Medina-Noyola, Magdaleno

Abstract

Our development of the effect of spatially nonlocal thermodynamic correlations on fluctuations is continued, focusing here on the hydrodynamic description for simple fluids. We use the canonical fluctuation-dissipation formalism and show that short ranged thermodynamic correlations are systematically included in the hydrodynamic description. In general the theory requires a knowledge of the second functional derivatives of the entropy - or equivalently - the two, three, and four point equilibrium correlation functions. For hard spheres this degenerates to a knowledge of the equilibrium radial distribution function. Within the context of the hydrodynamic theory, we present an exact calculation of the intermediate scattering function for hard spheres and compare with recent results from computer molecular dynamics. At liquid densities quantitative agreement is found as a function of time for distance scales up to the order of the hard sphere diameter. As expected, the time dependence of the fluctuating hydrodynamics results is only qualitatively correct for wavelengths much shorter than interactomic spacings or at interatomic spacings in the domain of gas densities. The implications of spatially nonlocal effects far from equilibrium is discussed.

Suggested Citation

  • Keizer, Joel & Medina-Noyola, Magdaleno, 1982. "Spatially nonlocal fluctuation theories: Hydrodynamic fluctuations for simple fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 301-338.
    • Handle: RePEc:eee:phsmap:v:115:y:1982:i:3:p:301-338
    DOI: 10.1016/0378-4371(82)90027-9
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    References listed on IDEAS

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    1. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    2. Medina-Noyola, Magdaleno & Keizer, Joel, 1981. "Spatial correlations in nonequilibrium systems: The effect of diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(3), pages 437-463.
    3. Weissman, James C. & Giacinti, Thomas A. & Lanasa, Francis W., 1973. "Undetected opiate use: A comparison of official drug user files and a private methadone clinic's patient records," Journal of Criminal Justice, Elsevier, vol. 1(2), pages 135-144.
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    Cited by:

    1. Keizer, Joel & Peacock-Lopez, Enrique, 1987. "Energy transport effects on rapid bimolecular chemical reactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 61-76.

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