IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v154y1989i3p452-466.html
   My bibliography  Save this article

Brownian motion in a medium with inhomogeneous temperature

Author

Listed:
  • Widder, M.E.
  • Titulaer, U.M.

Abstract

We consider the motion of a Brownian particle in a medium with inhomogeneous temperature in the presence of an external potential. We start from the Klein-Kramers equation; in this equation a thermophoretic force, proportional to the temperature gradient, should in general be included to obtain a correct description of thermodiffusion effects in the hydrodynamic stage of the evolution. With the Chapman-Enskog method we derive the correct form for the Smoluchowski equation, which reduces to van Kampen's recent result in the absence of thermophoretic forces. We also give the first correction to this equation caused by deviations from local thermal equilibrium. For the system considered, such deviations persist even in the steady state.

Suggested Citation

  • Widder, M.E. & Titulaer, U.M., 1989. "Brownian motion in a medium with inhomogeneous temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 154(3), pages 452-466.
    • Handle: RePEc:eee:phsmap:v:154:y:1989:i:3:p:452-466
    DOI: 10.1016/0378-4371(89)90259-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437189902598
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(89)90259-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Van Kampen, N.G., 1988. "Ten theorems about quantum mechanical measurements," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 153(1), pages 97-113.
    2. Landauer, Carl, 1972. "Die amerikanische Wirtschaftslage und die Präsidentenwahl," Wirtschaftsdienst – Zeitschrift für Wirtschaftspolitik (1949 - 2007), ZBW - Leibniz Information Centre for Economics, vol. 52(5), pages 259-262.
    3. Van Kampen, N.G., 1987. "A set of oscillators in a common bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 165-183.
    4. Skinner, James L. & Wolynes, Peter G., 1979. "Derivation of Smoluchowski equations with corrections for Fokker-Planck and BGK collision models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 96(3), pages 561-572.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pflügl, W & Titulaer, U.M, 1993. "The size distribution of liquid droplets during their growth from a vapor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 410-422.
    2. Bringuier, E., 2011. "Gauge-invariant approach to thermodiffusion in a liquid binary mixture," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1861-1875.
    3. Pflügl, W. & Titulaer, U.M., 1995. "The droplet size distribution in the late stage of phase separation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(1), pages 52-67.
    4. Kosztołowicz, Tadeusz, 1998. "Continuous versus discrete description of the transport in a membrane system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 44-56.
    5. Hui-Yun, Pan & Hai Jun, Wang, 1996. "A two-species surface reaction model of the mixing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(3), pages 234-238.
    6. Belan, S., 2016. "Concentration of diffusional particles in viscous boundary sublayer of turbulent flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 128-136.
    7. Zhong, Yuheng & Zhong, Weirong, 2024. "Inverse thermodiffusion of active matter in temperature gradient systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    8. Albano, Ezequiel V., 1995. "Irreversible phase transitions into non-unique absorbing states in a multicomponent reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(3), pages 426-434.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Titulaer, U.M., 1980. "Corrections to the Smoluchowski equation in the presence of hydrodynamic interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(2), pages 251-265.
    2. Stewart, Glen R., 1982. "Long-time behavior of a non-Markovian Brownian oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 519-530.
    3. Felderhof, B.U., 1983. "Reciprocity in electrohydrodynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 383-396.
    4. Vollmer, H.D. & Risken, H., 1982. "Eigenvalues and eigenfunctions of the Kramers equation. Application to the Brownian motion of a pendulum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 110(1), pages 106-127.
    5. Bunde, Armin & Gouyet, Jean-François, 1985. "Brownian motion in the bistable potential at intermediate and high friction: Relaxation from the instability point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 357-374.
    6. El Naschie, Mohamed Saladin, 2006. "The idealized quantum two-slit gedanken experiment revisited—Criticism and reinterpretation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 843-849.
    7. Janssen, J.A.M., 1988. "Solution of Kramers' problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 152(1), pages 145-176.
    8. Van Vliet, Carolyne M., 1990. "Quantum electrodynamical theory of infrared effects in condensed matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 126-155.
    9. Kosztołowicz, Tadeusz, 1998. "Continuous versus discrete description of the transport in a membrane system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 248(1), pages 44-56.
    10. Marchesoni, Fabio & Grigolini, Paolo, 1983. "The Kramers model of chemical relaxation in the presence of a radiation field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 269-285.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:154:y:1989:i:3:p:452-466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.