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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.

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Author:Jae-Hyung Jeon, Ralf MetzlerORCiDGND
ISSN:1539-3755 (print)
Parent Title (English):Physical review : E, Statistical, nonlinear and soft matter physics
Publisher:American Physical Society
Place of publication:College Park
Document Type:Article
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Funder:Academy of Finland
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert