Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
- Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.
| Author details: | Jae-Hyung Jeon, Ralf MetzlerORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1103/PhysRevE.85.021147 |
| ISSN: | 1539-3755 |
| Title of parent work (English): | Physical review : E, Statistical, nonlinear and soft matter physics |
| Publisher: | American Physical Society |
| Place of publishing: | College Park |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2012 |
| Publication year: | 2012 |
| Release date: | 2017/03/26 |
| Volume: | 85 |
| Issue: | 2 |
| Number of pages: | 8 |
| Funding institution: | Academy of Finland |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer review: | Referiert |
