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Kinetic equations of interacting Brownian particles

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  • Rudyak, Valeri
  • Ershov, Igor

Abstract

The dynamics of a single Brownian particle and an ensemble of such particles in an equilibrium bath is considered. Starting from the Liouville equation of the system, the corresponding kinetic equations are derived. To that end the simple perturbation method on a small parameter λ = √m/M is worked out (here m and M are the mass of the carrier medium molecule and Brownian particle, respectively). The kinetic equation of a single Brownian particle is obtained in second order of perturbation. It is shown that the kinetic equation of an ensemble of Brownian particles is in principle a nonlocal equation. It does not reduce to the Fokker-Plank equation even if direct particle-particle interactions are absent.

Suggested Citation

  • Rudyak, Valeri & Ershov, Igor, 1995. "Kinetic equations of interacting Brownian particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 351-360.
    • Handle: RePEc:eee:phsmap:v:219:y:1995:i:3:p:351-360
    DOI: 10.1016/0378-4371(95)00091-K
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    References listed on IDEAS

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    1. Oppenheim, Felix E., 1971. "Comment: Defense of Noncognitivism Defended," American Political Science Review, Cambridge University Press, vol. 65(4), pages 1115-1116, December.
    2. Fedyanin, V.K. & Gavrilenko, G.M., 1979. "On a derivation of the Fokker-Planck equation for a system weakly interacting with the heat bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 34-46.
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