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Microreversibility and driven Brownian motion with hydrodynamic long-time correlations

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  • Gaspard, Pierre

Abstract

A nonequilibrium fluctuation theorem is established for a colloidal particle driven by an external force within the hydrodynamic theory of Brownian motion, describing hydrodynamic memory effects such as the t−3∕2 power-law decay of the velocity autocorrelation function. The generalized Langevin equation is obtained for the general case of slip boundary conditions between the particle and the fluid. The Gaussian probability distributions for the particle to evolve in position–velocity space are deduced. It is proved that the joint probability distributions of forward and time-reversed paths have a ratio depending only on the work performed by the external force and the fluid temperature, in spite of the non-Markovian character of the generalized Langevin process.

Suggested Citation

  • Gaspard, Pierre, 2020. "Microreversibility and driven Brownian motion with hydrodynamic long-time correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 552(C).
    • Handle: RePEc:eee:phsmap:v:552:y:2020:i:c:s0378437119310659
    DOI: 10.1016/j.physa.2019.121823
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    References listed on IDEAS

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    1. Thomas Franosch & Matthias Grimm & Maxim Belushkin & Flavio M. Mor & Giuseppe Foffi & László Forró & Sylvia Jeney, 2011. "Resonances arising from hydrodynamic memory in Brownian motion," Nature, Nature, vol. 478(7367), pages 85-88, October.
    2. Bedeaux, D. & Albano, A.M. & Mazur, P., 1977. "Brownian motion and fluctuating hydrodynamics II; A fluctuation-dissipation theorem for the slip coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 88(3), pages 574-582.
    3. Felderhof, B.U., 1976. "Force density induced on a sphere in linear hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 569-576.
    4. Felderhof, B.U., 1976. "Force density induced on a sphere in linear hydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 557-568.
    5. Fodor, Étienne & Grebenkov, Denis S. & Visco, Paolo & van Wijland, Frédéric, 2015. "Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 107-112.
    6. Albano, A.M. & Bedeaux, D. & Mazur, P., 1975. "On the motion of a sphere with arbitrary slip in a viscous incompressible fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 80(1), pages 89-97.
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