Abstract
We investigate self-diffusion in a classical fluid composed of two species which are distinguished through the color of their particles, either black or white, but are identical as regards their mechanical properties. Disregarding color the fluid is in thermal equilibrium. We show that if a single “test particle” in the one-component fluid moves asymptotically as Brownian motion, then the color density and current in certain classes of nonequilibrium states are related, on the appropriate macroscopic scale, through Fick's law, and the former is governed by the diffusion equation. If in addition several test particles move asymptotically as independent Brownian motions, then the colored fluid is, on a macroscopic scale, in local equilibrium with parameters governed by the solution of the diffusion equation.
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Part of this work was done while both authors were at IHES, Bures-sur-Yvette, France.
Supported in part by NSF Grant No. PHY 78-15920-02.
Supported by a Heisenberg fellowship of the Deutsche Forschungsgemeinschaft.
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Lebowitz, J.L., Spohn, H. Microscopic basis for Fick's law for self-diffusion. J Stat Phys 28, 539–556 (1982). https://doi.org/10.1007/BF01008323
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DOI: https://doi.org/10.1007/BF01008323