Aging and nonergodicity beyond the Khinchin theorem

S. Burov, R. Metzler, E. Barkai

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144 Scopus citations


The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin's theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.

Original languageEnglish
Pages (from-to)13228-13233
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number30
StatePublished - 27 Jul 2010


  • Anomalous diffusion
  • Continuous time random walk
  • Ergodicity breaking
  • Irreversibility
  • Single particle trajectories


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