{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T01:57:11Z","timestamp":1771898231734,"version":"3.50.1"},"reference-count":14,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T00:00:00Z","timestamp":1354060800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 (DH). A detailed derivation for the calculation of DH is provided. The results are discussed for four variations of the crop farming system, showing that the efficiency of crop farming can be expressed by eSEA.<\/jats:p>","DOI":"10.3390\/e14122413","type":"journal-article","created":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T11:03:39Z","timestamp":1354100619000},"page":"2413-2426","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["The Extension of Statistical Entropy Analysis to Chemical Compounds"],"prefix":"10.3390","volume":"14","author":[{"given":"Alicja","family":"Soba\u0144tka","sequence":"first","affiliation":[{"name":"Centre for Water Resource Systems, Vienna University of Technology, Karlsplatz 13\/E222, A-1040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Zessner","sequence":"additional","affiliation":[{"name":"Centre for Water Resource Systems, Vienna University of Technology, Karlsplatz 13\/E222, A-1040 Vienna, Austria"},{"name":"Institute for Water Quality, Resource and Waste Management, Vienna University of Technology, Karlsplatz 13\/226, A-1040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helmut","family":"Rechberger","sequence":"additional","affiliation":[{"name":"Centre for Water Resource Systems, Vienna University of Technology, Karlsplatz 13\/E222, A-1040 Vienna, Austria"},{"name":"Institute for Water Quality, Resource and Waste Management, Vienna University of Technology, Karlsplatz 13\/226, A-1040 Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,11,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Baccini, P., and Brunner, H.P. (1991). Metabolism of the Anthroposphere, Springer.","DOI":"10.1007\/978-3-662-02693-9"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1021\/es010030h","article-title":"A new, entropy based method to support waste and resource management decisions","volume":"34","author":"Rechberger","year":"2002","journal-title":"Environ. Sci. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0921-8009(02)00102-7","article-title":"The contemporary European copper cycle: statistical entropy analysis","volume":"42","author":"Rechberger","year":"2002","journal-title":"Ecol. Econ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell System Technol. J."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Brunner, P.H., and Rechberger, H. (2004). 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Bundesministerium f\u00fcr Land- und Forstwirtschaft, Umwelt und Wasserwirtschaft.Verordnung des Bundesministers f\u00fcr Land-und Forstwirtschaft, Umwelt und Wasserwirtschaft \u00fcber die Festlegung des chemischen Zustandes f\u00fcr Oberfl\u00e4chengew\u00e4sser Teil II (BGBl. II Nr. 461\/2010)."},{"key":"ref_14","unstructured":"(2010). Bundesministerium f\u00fcr Land-und Forstwirtschaft, Umwelt und Wasserwirtschaft. Verordnung des Bundesministers f\u00fcr Land-und Forstwirtschaft, Umwelt und Wasserwirtschaft \u00fcber die Festlegung des chemischen Zustandes f\u00fcr Grundw\u00e4sser Teil II (BGBl. 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