Mean back relaxation for position and densities
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 1/2 has been shown to be a marker for breakage o...
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Veröffentlicht in: | Physical review. E 2024-10, Vol.110 (4-1), p.044137, Article 044137 |
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creator | Knotz, Gabriel Krüger, Matthias |
description | 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 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 cutoff 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 1/2 is a marker for broken detailed balance in confinement or in bulk systems. |
doi_str_mv | 10.1103/PhysRevE.110.044137 |
format | Article |
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title | Mean back relaxation for position and densities |
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