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Tsallis Entropy Theory for Modeling in Water Engineering: A Review

1
Department of Biological and Agricultural Engineering, Texas A&M University, College Station, TX 77843-2117, USA
2
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843-2117, USA
3
School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia
4
Department of Land, Air and Water Resources, University of California, Davis, CA 95616, USA
5
Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
*
Authors to whom correspondence should be addressed.
Entropy 2017, 19(12), 641; https://doi.org/10.3390/e19120641
Received: 15 September 2017 / Revised: 15 November 2017 / Accepted: 23 November 2017 / Published: 27 November 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
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Abstract

Water engineering is an amalgam of engineering (e.g., hydraulics, hydrology, irrigation, ecosystems, environment, water resources) and non-engineering (e.g., social, economic, political) aspects that are needed for planning, designing and managing water systems. These aspects and the associated issues have been dealt with in the literature using different techniques that are based on different concepts and assumptions. A fundamental question that still remains is: Can we develop a unifying theory for addressing these? The second law of thermodynamics permits us to develop a theory that helps address these in a unified manner. This theory can be referred to as the entropy theory. The thermodynamic entropy theory is analogous to the Shannon entropy or the information theory. Perhaps, the most popular generalization of the Shannon entropy is the Tsallis entropy. The Tsallis entropy has been applied to a wide spectrum of problems in water engineering. This paper provides an overview of Tsallis entropy theory in water engineering. After some basic description of entropy and Tsallis entropy, a review of its applications in water engineering is presented, based on three types of problems: (1) problems requiring entropy maximization; (2) problems requiring coupling Tsallis entropy theory with another theory; and (3) problems involving physical relations. View Full-Text
Keywords: entropy; water engineering; Tsallis entropy; principle of maximum entropy; Lagrangian function; probability distribution function; flux concentration relation entropy; water engineering; Tsallis entropy; principle of maximum entropy; Lagrangian function; probability distribution function; flux concentration relation
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Singh, V.P.; Sivakumar, B.; Cui, H. Tsallis Entropy Theory for Modeling in Water Engineering: A Review. Entropy 2017, 19, 641.

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