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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Online-Zugang: | https://arxiv.org/abs/2311.17477 |
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| _version_ | 1866929525983543296 |
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| author | Knotz, Gabriel Krüger, Matthias |
| author_facet | Knotz, Gabriel Krüger, Matthias |
| contents | Correlation functions are a standard tool for analyzing statistical particle trajectories. Recently, a so called mean back relaxation (MBR) has been introduced, which correlates positions at three time points. The deviation of its long time value from $\frac{1}{2}$ has been shown to be a marker for breakage of time reversal symmetry for confined particles. Here, we extend the analysis of MBR in several ways, including discussion of a cut off length used when evaluating MBR from trajectory data. Using a path integral approach, we provide a general expression for MBR in terms of multipoint density correlations. For Gaussian systems, this expression yields a relation between MBR and mean squared displacement. We finally demonstrate that MBR can be applied to other stochastic observables besides particle position. Using it for microscopic densities, its deviation from $\frac{1}{2}$ is a marker for broken detailed balance in confinement or in bulk systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17477 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean Back Relaxation for Position and Densities Knotz, Gabriel Krüger, Matthias Statistical Mechanics Correlation functions are a standard tool for analyzing statistical particle trajectories. Recently, a so called mean back relaxation (MBR) has been introduced, which correlates positions at three time points. The deviation of its long time value from $\frac{1}{2}$ has been shown to be a marker for breakage of time reversal symmetry for confined particles. Here, we extend the analysis of MBR in several ways, including discussion of a cut off length used when evaluating MBR from trajectory data. Using a path integral approach, we provide a general expression for MBR in terms of multipoint density correlations. For Gaussian systems, this expression yields a relation between MBR and mean squared displacement. We finally demonstrate that MBR can be applied to other stochastic observables besides particle position. Using it for microscopic densities, its deviation from $\frac{1}{2}$ is a marker for broken detailed balance in confinement or in bulk systems. |
| title | Mean Back Relaxation for Position and Densities |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2311.17477 |