标题： 通过平均反向弛豫评估非平衡轨迹：长度和时间尺度的依赖性 显示英文标题

标题： Evaluating non-equilibrium trajectories via mean back relaxation: Dependence on length and time scales

摘要： 平均反向弛豫（MBR）将随机过程在三个不同时间点的值联系起来。 在某些条件下，它已被证明可以检测破坏细致平衡的情况。 对于活细胞和钝化细胞中的探测粒子实验，发现MBR与所谓的有效能量有关，该有效能量量化了涨落耗散定理的违背程度。 在本文中，我们讨论进入MBR的长度和时间参数的依赖性，适用于细胞以及一个模型系统，发现两者之间有定性一致的结果。 对于细胞数据，我们将MBR与有效能量之间的现象学关系扩展到比之前工作更广泛的时间参数范围，从而可以在分辨率有限的系统中对其进行测试。 我们分析了反向弛豫方差（VBR）与上述参数的依赖关系，这对于MBR评估中的统计误差是相关的。 对于高斯系统，方差在均方位移的基础上被解析地找到，并且我们确定了其作为长度和时间参数函数的绝对最小值。 将细胞数据中的VBR与高斯预测进行比较，表明这是一个非高斯过程。 显示英文摘要

摘要： The mean back relaxation (MBR) relates the value of a stochastic process at three different time points. It has been shown to detect broken detailed balance under certain conditions. For experiments of probe particles in living and passivated cells, MBR was found to be related to the so called effective energy, which quantifies the violation of the fluctuation dissipation theorem. In this manuscript, we discuss the dependence on the length and time parameters that enter MBR, both for cells as well as for a model system, finding qualitative agreement between the two. For the cell data, we extend the phenomenological relation between MBR and effective energy to a larger range of time parameters compared to previous work, allowing to test it in systems with limited resolution. We analyze the variance of back relaxation (VBR) in dependence of the mentioned parameters, relevant for the statistical error in MBR evaluation. For Gaussian systems, the variance is found analytically in terms of the mean squared displacement, and we determine its absolute minimum as a function of the length and time parameters. Comparing VBR from cell data to a Gaussian prediction demonstrates a non-Gaussian process.