Weakly Non-Ergodic Statistical Physics |
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Authors: | A Rebenshtok E Barkai |
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Institution: | (1) Department of Physics, Bar Ilan University, Ramat-Gan, 52900, Israel |
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Abstract: | For weakly non ergodic systems, the probability density function of a time average observable
is
where
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
j
eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x
2〉∼t
α
found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered
. We briefly discuss possible physical applications in single particle experiments. |
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Keywords: | Weak ergodicity breaking Continuous time random walk Fractional Fokker– Planck equation |
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