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Spatial correlations in nonequilibrium systems: The effect of diffusion

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  • Medina-Noyola, Magdaleno
  • Keizer, Joel

Abstract

We show how the ideas of the fluctuation-dissipation theory can be used to calculate spatial correlations in interacting systems away from equilibrium. The only spatially dependent dissipative process considered is diffusion, and spatial correlations are generated by the nonlocal spatial dependence of the chemical potential. The results are the lowest order in a hierarchy of generalized hydrodynamic type calculations applicable to nonequilibrium systems. We derive equations for the density correlation functions at stationary state supported by diffusive fluxes and show that they have the local equilibrium form. The static correlation function is obtained from the fluctuation-dissipation theorem, which we show to be equivalent to the Ornstein-Zernike integral equation. At equilibrium we demonstrate that the dynamical structure factor obtained by these methods includes the expected wave-vector dependent diffusion constant. Finally we derive a necessary and sufficient condition for local equilibrium to obtain at a stationary state and show by explicit calculation that chemical processes can give rise to significant nonequilibrium correlations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:107:y:1981:i:3:p:437-463
    DOI: 10.1016/0378-4371(81)90181-3
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    Cited by:

    1. Keizer, Joel, 1983. "Steady state thermodynamics and spatial correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 118(1), pages 350-359.
    2. Keizer, Joel & Conlan, F.J., 1983. "A fine-grained master equation theory of chemical reaction fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 405-426.
    3. 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.

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