Origins of Taylor's power law for fluctuation scaling in complex systems

TL;DR

This paper provides a theoretical foundation for Taylor's fluctuation scaling law in complex systems, demonstrating its universality through statistical physics principles and validating with diverse real-world data.

Contribution

It establishes a fundamental link between Taylor's law and the density of states in complex systems, offering a unifying theoretical explanation.

Findings

Taylor's law results from the density of states function.

The approach is validated across ecological, traffic, financial, and biological data.

Theoretical foundations are grounded in statistical physics principles.

Abstract

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 strong theoretical foundations 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 non-equilibrium) we prove that Taylor's law results from the well-defined density of states (DOS) function of a system that gives the number of states 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).