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Stochastic processes originating in deterministic microscopic dynamics

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Abstract

We investigate the probability distribution of the scaled trajectory of a test particle moving in an equilibrium fluid according to the laws of classical mechanics, i.e., ifQ(t) is the displacement of the test particle we letQ A(t) =Q(At)/√A and consider the distribution of the trajectory QA(t) in the limit A→∞. The randomness of the motion is due entirely to the randomness of the initial state of the fluid, test particle, or both, and the process is generally non-Markovian. Nevertheless, it can be proven in some cases and we expect it to be true in many more that QA (t) looks like Brownian motion in the limit A→∞. Some results for simple model systems are presented.

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Author notes

  1. Detlef Dürr

    Present address: Fachbereich Mathematik, RUB, H630, Bochum

Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, New Jersey

    Detlef Dürr, Sheldon Goldstein & Joel L. Lebowitz

  2. Department of Physics, Rutgers University, New Brunswick, New Jersey

    Joel L. Lebowitz

Authors
  1. Detlef Dürr
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  2. Sheldon Goldstein
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  3. Joel L. Lebowitz
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Additional information

Supported in part by NSF Grants DMR 81-14726 and PHY 78-03816.

Supported by DFG Fellowship.

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Dürr, D., Goldstein, S. & Lebowitz, J.L. Stochastic processes originating in deterministic microscopic dynamics. J Stat Phys 30, 519–526 (1983). https://doi.org/10.1007/BF01012325

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