title: Universal flux-fluctuation law in small systems.
abstract: The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.
authors.affiliation: 1] Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China [2] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
authors.forename: Zi-Gang
authors.initials: ZG
authors.lastname: Huang
authors.affiliation: Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China.
authors.forename: Jia-Qi
authors.initials: JQ
authors.lastname: Dong
authors.affiliation: 1] Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China [2] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA.
authors.forename: Liang
authors.initials: L
authors.lastname: Huang
authors.affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] Department of Physics, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai