%0 Book Section %1 statphys23_0202 %A Bel, G. %A Barkai, E. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K ctrw ergodicity single-molecule statphys23 topic-1 %T Ergodicity Breaking in the Continuous Time Random Walk %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=202 %X The continuous-time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory in this case? Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory 1. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law. In particular we show that in the non-ergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. When conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the non-ergodic dynamics and canonical statistical mechanics. The relation of our work to single-molecule experiments is briefly discussed.\\ 1) G. Bel and E. Barkai, Phys. Rev. Lett., 94, 240602 (2005), Phys. Rev. E, 73, 016125 (2006).

@incollection{statphys23_0202, abstract = {The continuous-time random walk (CTRW) model exhibits a non-ergodic phase when the average waiting time diverges. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory in this case? Using an analytical approach for the non-biased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the non-ergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory [1]. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the non-ergodic phase yields a generalized non-ergodic statistical law. In particular we show that in the non-ergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. When conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the non-ergodic dynamics and canonical statistical mechanics. The relation of our work to single-molecule experiments is briefly discussed.\\ 1) G. Bel and E. Barkai, Phys. Rev. Lett., 94, 240602 (2005), Phys. Rev. E, 73, 016125 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Bel, G. and Barkai, E.}, biburl = {https://www.bibsonomy.org/bibtex/2cb0643a5fc9041206a6591e8ca21de8a/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {69eeee914dfd7e96d8d22c43842649ef}, intrahash = {cb0643a5fc9041206a6591e8ca21de8a}, keywords = {ctrw ergodicity single-molecule statphys23 topic-1}, month = {9-13 July}, timestamp = {2007-06-20T10:16:14.000+0200}, title = {Ergodicity Breaking in the Continuous Time Random Walk}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=202}, year = 2007 }