Magdziarz Marcin, Weron Aleksander
Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wroclaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Nov;84(5 Pt 1):051138. doi: 10.1103/PhysRevE.84.051138. Epub 2011 Nov 29.
Recent advances in single-molecule experiments show that various complex systems display nonergodic behavior. In this paper, we show how to test ergodicity and ergodicity breaking in experimental data. Exploiting the so-called dynamical functional, we introduce a simple test which allows us to verify ergodic properties of a real-life process. The test can be applied to a large family of stationary infinitely divisible processes. We check the performance of the test for various simulated processes and apply it to experimental data describing the motion of mRNA molecules inside live Escherichia coli cells. We show that the data satisfy necessary conditions for mixing and ergodicity. The detailed analysis is presented in the supplementary material.
单分子实验的最新进展表明，各种复杂系统都表现出非遍历性行为。在本文中，我们展示了如何在实验数据中测试遍历性和遍历性破坏。利用所谓的动态泛函，我们引入了一个简单的测试，它使我们能够验证现实生活过程的遍历性质。该测试可以应用于一大类平稳无限可分过程。我们检查了该测试对各种模拟过程的性能，并将其应用于描述活大肠杆菌细胞内mRNA分子运动的实验数据。我们表明，这些数据满足混合和遍历性的必要条件。详细分析见补充材料。
