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Diffusive Spreading in Nature, Technology and Society pp 127–145Cite as

Hot Brownian Motion

Abstract

The chapter deals with hot Brownian particles and swimmers as two examples for Brownian motion very far from equilibrium. Thanks to the strong scale separation between the Brownian particles and the solvent atoms, substantial theoretical progress could be made along the lines first laid out by Einstein, yielding exact analytical predictions for hot Brownian dynamics by coarse graining. Wherever these predictions were tested, they were found in excellent agreement with experimental observations and simulation data. The chapter is as well dealing with the steering of hot swimmers by Maxwell-demon type methods summarily known as photon nudging. They enable experimentalists to tailor their interactions and to create micron-sized swarms of active particles serving as a microscopic laboratory for studying large-scale biological phenomena.

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Fig. 8.1
Fig. 8.2
Fig. 8.3
Fig. 8.4
Fig. 8.5
Fig. 8.6

Notes

  1. 1.

    For further introductory reading see Refs. [3,4,5,6]. The names of our collaborators (partly funded by the Deutsche Forschungsgemeinschaft and the Humboldt foundation), who did much of the original work reviewed here, can be found in the references, at the end.

  2. 2.

    The analogy might seem compelling, but the opponents of the atomistic world view would have objected to the application of thermodynamic notions to colloidal particles.

  3. 3.

    At the time of writing, Google Scholar lists more than 6000 citations.

  4. 4.

    The general expression for a non-spherical particle in an arbitrary temperature field is slightly more complex than Eq. (8.6), but its basic structure is the same [20].

  5. 5.

    Joseph Fourier assumed heat to diffuse, an idea adapted to particles by Adolf Fick in 1855.

  6. 6.

    We count incoming energies as positive in the first law of thermodynamics: \(\mathrm {d}U=\delta Q +\delta W\).

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Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Leipzig University, Leipzig, Germany

    Klaus Kroy

  2. Peter Debye Institute for Soft Matter Physics, Leipzig University, Leipzig, Germany

    Frank Cichos

Authors
  1. Klaus Kroy
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Correspondence to Klaus Kroy .

Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Justus-Liebig-Universität Gießen Institut für Theoretische Physik, Gießen, Germany

    Armin Bunde

  2. Inst. für Physikalische Chemie und Elektrochemie, Leibniz-Universität Hannover, Hannover, Germany

    Prof. Dr. Jürgen Caro

  3. Institut für Experimentalphysik I, Universität Leipzig Institut für Experimentalphysik I, Leipzig, Germany

    Jörg Kärger

  4. Inst. für Festkörperphysik, Universität Wien, Wien, Austria

    Prof. Dr. Gero Vogl

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Kroy, K., Cichos, F. (2018). Hot Brownian Motion. In: Bunde, A., Caro, J., Kärger, J., Vogl, G. (eds) Diffusive Spreading in Nature, Technology and Society. Springer, Cham. https://doi.org/10.1007/978-3-319-67798-9_8

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