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


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
StatePublished - 9 Dec 2011

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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