How related are the ergodic properties of the over- and underdamped Langevin equations driven by fractional Gaussian noise? We here find that for massive particles performing fractional Brownian motion (FBM) inertial effects not only destroy the stylized fact of the equivalence of the ensemble-averaged mean-squared displacement (MSD) to the time-averaged MSD (TAMSD) of overdamped or massless FBM, but also concurrently dramatically alter the values of the ergodicity breaking parameter (EB). Our theoretical results for the behavior of EB for underdamped ot massive FBM for varying particle mass m, Hurst exponent H, and trace length T are in excellent agreement with the findings of extensive stochastic computer simulations. The current results can be of interest for the experimental community employing various single-particle-tracking techniques and aiming at assessing the degree of nonergodicity for the recorded time series (studying e.g. the behavior of EB versus lag time). To infer FBM as a realizable model of anomalous diffusion for a set single-particle-tracking data when massive particles are being tracked, the EBs from the data should be compared to EBs of massive (rather than massless) FBM.

中文翻译：

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惯性触发分数布朗运动的非遍历性

分数高斯噪声驱动的过阻尼和欠阻尼朗之万方程的遍历特性之间的相关性如何？我们在这里发现，对于执行分数布朗运动 (FBM) 惯性效应的大质量粒子，不仅破坏了整体平均均方位移 (MSD) 与过阻尼或无质量的时间平均 MSD (TAMSD) 等价的程式化事实FBM，但同时也会显着改变遍历破坏参数 (EB) 的值。我们针对不同粒子质量m、Hurst 指数H和迹线长度T 的欠阻尼或大质量 FBM 的 EB 行为的理论结果与广泛的随机计算机模拟的结果非常一致。对于采用各种单粒子跟踪技术并旨在评估所记录时间序列的非遍历性程度（研究例如 EB 与滞后时间的行为）的实验社区，当前的结果可能会引起人们的兴趣。为了在跟踪大质量粒子时将 FBM 推断为一组单粒子跟踪数据的异常扩散的可实现模型，应将数据中的 EB 与大量（而不是无质量）FBM 的 EB 进行比较。