TY - JOUR

T1 - Aging and nonergodicity beyond the Khinchin theorem

AU - Burov, S.

AU - Metzler, R.

AU - Barkai, E.

PY - 2010/7/27

Y1 - 2010/7/27

N2 - 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.

AB - 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.

KW - Anomalous diffusion

KW - Continuous time random walk

KW - Ergodicity breaking

KW - Irreversibility

KW - Single particle trajectories

UR - http://www.scopus.com/inward/record.url?scp=77955785256&partnerID=8YFLogxK

U2 - 10.1073/pnas.1003693107

DO - 10.1073/pnas.1003693107

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C2 - 20624984

AN - SCOPUS:77955785256

SN - 0027-8424

VL - 107

SP - 13228

EP - 13233

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 30

ER -