论文标题
部分可观测时空混沌系统的无模型预测
Spatial correlation functions for non-ergodic stochastic processes of macroscopic system
论文作者
论文摘要
专注于非共性宏观系统，我们重新考虑时间序列的差异。已知总方差（在所有时间序列上的直接平均值）是内部差异（元巴asins内波动）和外部方差（元基础之间的波动）的总和。结果表明，每当可以观察到的时间平均值作为本地场的体积平均值时，可以将三个方差写入相关函数的音量平均值，而总相关函数是内部和外部相关函数的总和。因此，不同方差的依赖性可以追溯到内部和外部相关函数。使用具有空间相关的弹簧常数的晶格弹簧模型来说明各种关系。
Focusing on non-ergodic macroscopic systems we reconsider the variances of time averages time-series. The total variance (direct average over all time-series) is known to be the sum of an internal variance (fluctuations within the meta-basins) and an external variance (fluctuations between meta-basins). It is shown that whenever the time-averaged observable can be expressed as a volume average of a local field the three variances can be written as volume averages of correlation functions with the total correlation function being the sum of an internal and an external correlation function. The dependences of the the different variancescan thus be traced back to the internal and the external correlation function. Various relations are illustrated using lattice spring models with spatially correlated spring constants.
