Fluctuations of time averages for Langevin dynamics in a binding force field

A. Dechant, E. Lutz, D. A. Kessler, E. Barkai

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


We derive a simple formula for the fluctuations of the time average x̄(t) around the thermal mean x eq 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.

Original languageEnglish
Article number240603
JournalPhysical review letters
Issue number24
Publication statusPublished - 2011 Dec 9
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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