系综涨落对宏观变量的方差很重要。
Ensemble fluctuations matter for variances of macroscopic variables.
作者信息
George G, Klochko L, Semenov A N, Baschnagel J, Wittmer J P
机构信息
Institut Charles Sadron, Université de Strasbourg & CNRS, 23 rue du Loess, 67034, Strasbourg Cedex, France.
出版信息
Eur Phys J E Soft Matter. 2021 Mar 8;44(2):13. doi: 10.1140/epje/s10189-020-00004-7.
Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average [Formula: see text] and the standard deviation [Formula: see text] of the variance [Formula: see text] of time series [Formula: see text] of a stochastic process x(t) measured over a finite sampling time [Formula: see text]. Assuming a stationary, Gaussian and ergodic process, [Formula: see text] is given by a functional [Formula: see text] of the autocorrelation function h(t). [Formula: see text] is shown to become large and similar to [Formula: see text] if [Formula: see text] corresponds to a fast relaxation process. Albeit [Formula: see text] does not hold in general for non-ergodic systems, the deviations for common systems with many microstates are merely finite-size corrections. Various issues are illustrated for shear-stress fluctuations in simple coarse-grained model systems.
扩展近期关于复杂流体和非晶态固体中应力涨落的研究工作，我们用一般术语描述了在有限采样时间(\tau)内测量的随机过程(x(t))的时间序列({x(t)})的方差(\sigma^2(t))的系综平均(\langle\sigma^2\rangle)和标准差(\sigma)。假设过程是平稳、高斯且遍历的，(\langle\sigma^2\rangle)由自相关函数(h(t))的泛函(F[h])给出。如果(\tau)对应于快速弛豫过程，(\sigma)会变得很大且类似于(\langle\sigma^2\rangle)。尽管对于非遍历系统(\langle\sigma^2\rangle\neq\sigma^2)一般不成立，但对于具有许多微观状态的常见系统，偏差仅仅是有限尺寸修正。在简单的粗粒化模型系统中，针对剪应力涨落说明了各种问题。
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