Weak ergodicity breaking in the continuous-time random walk

G. Bel, E. Barkai

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263 Scopus citations


The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. Using an analytical approach for the nonbiased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the nonergodic phase yields a generalized nonergodic statistical law.

Original languageEnglish
Article number240602
JournalPhysical Review Letters
Issue number24
StatePublished - 24 Jun 2005


FundersFunder number
National Science Foundation
Directorate for Mathematical and Physical Sciences0344930


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