Conditional Ergodicity and Universal Fluctuations in Weak Ergodicity Breaking
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| Format: | Preprint |
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2026
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| _version_ | 1866911521728102400 |
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| author | Shafir, Dan Burov, Stanislav |
| author_facet | Shafir, Dan Burov, Stanislav |
| contents | Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in anomalous diffusion and signals weak ergodicity breaking driven by scale-free trapping. Here we identify conditional ergodicity: conditioning on a natural internal clock restores self-averaging of time-averaged observables. Combining conditional ergodicity with the stochastic mapping between the internal clock and physical time implies a universal law: once rescaled by their mean, time-averaged transport coefficients in systems exhibiting weak ergodicity breaking follow the Mittag-Leffler distribution. We demonstrate this universality across multiple models of disordered media displaying anomalous diffusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_16121 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conditional Ergodicity and Universal Fluctuations in Weak Ergodicity Breaking Shafir, Dan Burov, Stanislav Statistical Mechanics Disordered Systems and Neural Networks Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in anomalous diffusion and signals weak ergodicity breaking driven by scale-free trapping. Here we identify conditional ergodicity: conditioning on a natural internal clock restores self-averaging of time-averaged observables. Combining conditional ergodicity with the stochastic mapping between the internal clock and physical time implies a universal law: once rescaled by their mean, time-averaged transport coefficients in systems exhibiting weak ergodicity breaking follow the Mittag-Leffler distribution. We demonstrate this universality across multiple models of disordered media displaying anomalous diffusion. |
| title | Conditional Ergodicity and Universal Fluctuations in Weak Ergodicity Breaking |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2603.16121 |