Abstract
Previous work by Hauge and Martin-Löf discussing the generalized Langevin equation for Brownian motion as a contraction from the more fundamental but still phenomenological description of a particle immersed in an incompressible fluid governed by fluctuating hydrodynamics with stick boundary condition is extended to the case of a Brownian particle with arbitrary shape and withslip boundary condition. The motivation for this extension is the fact that the latter condition naturally arises in a treatment of the problem from first principles.
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E. H. Hauge and A. Martin-Löf,J. Stat. Phys. 7(3):259 (1973).
L. D. Landau and E. M. Lifshitz,Fluid Mechanics, Pergamon Press, London (1959), p. 67.
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Velarde, M.G., Hauge, E.H. Fluctuating hydrodynamics and Brownian motion. II. Note on the slip boundary condition. J Stat Phys 10, 103–105 (1974). https://doi.org/10.1007/BF01011720
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DOI: https://doi.org/10.1007/BF01011720