Universal flux-fluctuation law in small systems

Zi-Gang Huang, Jia-Qi Dong, Liang Huang, Ying-Cheng Lai

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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.
Original languageEnglish
Article number6787
JournalScientific Reports
Publication statusPublished - 27 Dec 2014

Bibliographical note

We thank Dr. DeMenezes for providing the microchip data. This work was partially
supported by the NSF of China under Grant Nos. 11135001, 11275003. Y.C.L. was
supported by ARO under Grant No. W911NF-14-1-0504.


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