Fronczak Agata, Fronczak Piotr
Faculty of Physics, Warsaw University of Technology, PL-00-662 Warsaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):066112. doi: 10.1103/PhysRevE.81.066112. Epub 2010 Jun 17.
Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor's FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor's law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).
泰勒涨落标度律（FS）已在许多自然和人造系统中被观测到，揭示了该定律惊人的普遍性。在此，我们对泰勒FS在不同复杂系统中的起源和普遍性给出了可靠的解释。我们的方法的普遍性通过来自现实世界的数据得到验证，这些数据涵盖从鸟类和昆虫种群、人类染色体、交通网络中的交通流量到股票市场动态等各个领域。利用统计物理学的基本原理（包括平衡态和非平衡态），我们证明泰勒定律源于一个系统具有明确数量的状态，这些状态由一个宏观参数的相同值所表征（例如，在给定区域观察到的鸟类数量、以通过给定观测点的汽车数量衡量的交通流量或股票市场中以数百万美元衡量的每日活动）。
