Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-07-26
Phys. Rev. Letters 99, 210601 (2007)
Physics
Condensed Matter
Statistical Mechanics
5 pages, 2 figures
Scientific paper
10.1103/PhysRevLett.99.210601
We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $
Barkai Eli
Rebenshtok Adi
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