No-go theorem for ergodicity and an Einstein relation

D. Froemberg, E. Barkai

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


We provide a simple no-go theorem for ergodicity and the generalized Einstein relation for anomalous diffusion processes. The theorem states that either ergodicity in the sense of equal time and ensemble averaged mean squared displacements (MSD) is broken, and/or the generalized Einstein relation for time averaged diffusivity and mobility is invalid, which is in complete contrast to normal diffusion processes. We also give a general relation for the time averages of drift and MSD for ergodic (in the MSD sense) anomalous diffusion processes, showing that the ratio of these quantities depends on the measurement time. The Lévy walk model is used to exemplify the no-go theorem.

Original languageEnglish
Article number024101
Pages (from-to)024101
JournalPhysical Review E
Issue number2
StatePublished - 5 Aug 2013


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