Weakly non-ergodic statistical physics

A. Rebenshtok, E. Barkai

Research output: Contribution to journalArticlepeer-review

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Abstract

For weakly non ergodic systems, the probability density function of a time average observable Script O sign is fα(Script O sign) = (Equation Presented) where Script O signj is the value of the observable when the system is in state j=1,... L. p j eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p jeq is Boltzmann's cnonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0 < α < 1 is the anomalous diffusion exponent 〈x2〉 ∼tα found for free boundary conditions. When α → 1 ergodic statistical mechanics is recovered limα→1 fα(Script O sign) = δ(Script O sign - 〈Script O sign〉). We briefly discuss possible physical applications in single particle experiments.

Original languageEnglish
Pages (from-to)565-586
Number of pages22
JournalJournal of Statistical Physics
Volume133
Issue number3
StatePublished - Nov 2008

Bibliographical note

Funding Information:
Acknowledgements This work was supported by the Israel Science Foundation. E.B. thanks G. Margolin, S. Burov, and G. Bel for discussions.

Funding

Acknowledgements This work was supported by the Israel Science Foundation. E.B. thanks G. Margolin, S. Burov, and G. Bel for discussions.

FundersFunder number
Israel Science Foundation

    Keywords

    • Continuous time random walk
    • Fractional Fokker-Planck equation
    • Weak ergodicity breaking

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