A Random Walk to a Non-Ergodic Equilibrium Concept
| dc.creator | Bel, Golan | |
| dc.creator | Barkai, Eli | |
| dc.date | 2005-06-14 | |
| dc.date.accessioned | 2026-07-07T06:25:55Z | |
| dc.date.available | 2026-07-07T06:25:55Z | |
| dc.description | Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this manuscript a non-ergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the non-ergodic phase the distribution of the occupation time of the particle on a given lattice point, approaches U or W shaped distributions related to the arcsin law. We show that 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. In the ergodic phase the distribution function of the occupation times approaches a delta function centered on the value predicted based on standard Boltzmann-Gibbs statistics. Relation of our work with single molecule experiments is briefly discussed. | |
| dc.description | 14 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0506338 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0506338 | |
| dc.identifier | Phys. Rev. E 73, 016125 (2006) | |
| dc.identifier | doi:10.1103/PhysRevE.73.016125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96968 | |
| dc.subject | Statistical Mechanics | |
| dc.title | A Random Walk to a Non-Ergodic Equilibrium Concept | |
| dc.type | text |