Spatially nonlocal fluctuation theories: Hydrodynamic fluctuations for simple fluids

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. © 1982.

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