the extension of statistical entropy analysis to chemical compounds扩展的统计熵分析化合物.pdf

Entropy 2012, 14, 2413-2426; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article The Extension of Statistical Entropy Analysis to Chemical Compounds Alicja P. Sobańtka 1, Matthias Zessner 1,2 and Helmut Rechberger 1,2,* 1 Centre for Water Resource Systems, Vienna University of Technology, Karlsplatz 13/E222, A-1040 Vienna, Austria; E-Mail: sobantka@waterresources.at (A.P.S.) 2 Institute for Water Quality, Resource and Waste Management, Vienna University of Technology, Karlsplatz 13/226, A-1040 Vienna, Austria; E-Mail: m.zessner@iwag.tuwien.ac.at (M.Z.) * Author to whom correspondence should be addressed; E-Mail: helmut.rechberger@tuwien.ac.at; Tel.: +43-1-58 801-226 45; Fax: +43-1-58 801-226 97. Received: 23 August 2012; in revised form: 25 September 2012 / Accepted: 26 November 2012 / Published: 28 November 2012 Abstract: Statistical entropy analysis (SEA) quantifies the dilution and concentration of conservative substances (e.g., heavy metals) in a system. In this paper, the SEA concept is extended (eSEA) to make it applicable to systems in which the chemical speciation is of particular importance. The eSEA is applied to a simplified region used for crop farming. The extent to which the region concentrates or dilutes nitrogen compounds is expressed as the change in statistical entropy (H). A detailed derivation for the calculation of H is provided. The results are discussed for four variations of the crop farming system, showing that the efficiency of crop farming can