Entropy 2013, 15(1), 327-360; doi:10.3390/e15010327
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The Liang-Kleeman Information Flow: Theory and Applications

1 School of Marine Sciences and School of Mathematics and Statistics, Nanjing University of Information Science and Technology (Nanjing Institute of Meteorology), 219 Ningliu Blvd, Nanjing 210044, China 2 China Institute for Advanced Study, Central University of Finance and Economics, 39 South CollegeAve, Beijing 100081, China 
Received: 17 October 2012; in revised form: 22 November 2012 / Accepted: 28 December 2012 / Published: 18 January 2013
(This article belongs to the Special Issue Transfer Entropy)
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Abstract: Information flow, or information transfer as it may be referred to, is a fundamental notion in general physics which has wide applications in scientific disciplines. Recently, a rigorous formalism has been established with respect to both deterministic and stochastic systems, with flow measures explicitly obtained. These measures possess some important properties, among which is flow or transfer asymmetry. The formalism has been validated and put to application with a variety of benchmark systems, such as the baker transformation, Hénon map, truncated Burgers-Hopf system, Langevin equation, etc. In the chaotic Burgers-Hopf system, all the transfers, save for one, are essentially zero, indicating that the processes underlying a dynamical phenomenon, albeit complex, could be simple. (Truth is simple.) In the Langevin equation case, it is found that there could be no information flowing from one certain time series to another series, though the two are highly correlated. Information flow/transfer provides a potential measure of the cause–effect relation between dynamical events, a relation usually hidden behind the correlation in a traditional sense.
Keywords: Liang-Kleeman information flow; causation; emergence; Frobenius-Perron operator; time series analysis; atmosphere-ocean science; El Niño; neuroscience; network dynamics; financial economics

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MDPI and ACS Style

Liang, X.S. The Liang-Kleeman Information Flow: Theory and Applications. Entropy 2013, 15, 327-360.

AMA Style

Liang XS. The Liang-Kleeman Information Flow: Theory and Applications. Entropy. 2013; 15(1):327-360.

Chicago/Turabian Style

Liang, X. S. 2013. "The Liang-Kleeman Information Flow: Theory and Applications." Entropy 15, no. 1: 327-360.

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