Abstract
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 language | English |
|---|---|
| Article number | 240603 |
| Journal | Physical Review Letters |
| Volume | 107 |
| Issue number | 24 |
| DOIs | |
| Publication status | Published - 2011 Dec 9 |
| Externally published | Yes |
ASJC Scopus subject areas
- Physics and Astronomy(all)
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Dechant, A., Lutz, E., Kessler, D. A., & Barkai, E. (2011). Fluctuations of time averages for Langevin dynamics in a binding force field. Physical Review Letters, 107(24), [240603]. https://doi.org/10.1103/PhysRevLett.107.240603