Fluctuations of Time Averages for Langevin Dynamics in a Binding Force Field

A. Dechant, E. Lutz, D. A. Kessler, and E. Barkai
Phys. Rev. Lett. 107, 240603 – Published 9 December 2011

Abstract

We derive a simple formula for the fluctuations of the time average x¯(t) around the thermal mean xeq for overdamped Brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.

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  • Received 3 June 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.240603

© 2011 American Physical Society

Authors & Affiliations

A. Dechant and E. Lutz

  • Department of Physics, University of Augsburg, D-86135 Augsburg, Germany

D. A. Kessler and E. Barkai

  • Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel

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Vol. 107, Iss. 24 — 9 December 2011

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