{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T13:27:40Z","timestamp":1772112460120,"version":"3.50.1"},"reference-count":74,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T00:00:00Z","timestamp":1671494400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["869318"],"award-info":[{"award-number":["869318"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Our work analyzes the biophysical and economic foundations of the Sherwood Plot (SP). In general, the SP depicts the theoretical relationship between the cost of recovering a target material or an identified Value Added Compound (VAC) from a waste matrix and its dilution in the waste matrix; specifically suggesting that the recovery cost is reverse proportional to the VAC\u2019s dilution in it. We further utilize the SP as a scientifically consistent and economically coherent analytical framework for measuring resource recovery performance. Initially, we analyze the SP\u2019s fundamental physical properties, as well as its many potential economic extensions. Specifically, we substantiate the relation between a VAC\u2019s Entropy, Dilution and Recovery Cost. On these grounds we present the SP\u2019s remarkable and numerous economic properties that make it consistent to its physical foundations; thus integrating concisely its physical and economic aspects and postulate a generalized SP function. We further test econometrically the validity of an SP based on both deterministic and stochastic real data from a small-scale industrial unit of polyphenols\u2019 recovery from natural fruit juice production residual wastewater. In turn, based on the fusion of our theoretical argumentation and empirical findings we dive into the epistemological extensions of the SP. Specifically, we study how the recovery cost structure at the single industry level is revealed by the SP and can be useful for postulating cost structure ontologies. Cost ontologies are in turn useful as a diagnostic of the formation process of VAC recovery markets as well as their structure and concentration, defining the industrial shares when many industries operate in the recovery of the same VAC.<\/jats:p>","DOI":"10.3390\/e25010004","type":"journal-article","created":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T05:08:54Z","timestamp":1671512934000},"page":"4","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Resource Recovery and the Sherwood Plot"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1449-1747","authenticated-orcid":false,"given":"Georgios","family":"Karakatsanis","sequence":"first","affiliation":[{"name":"Department of Research, EVOTROPIA Ecological Finance Architectures Private Company (P.C.), 190 Syngrou Avenue, 17671 Kallithea, Greece"},{"name":"Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechneiou St., 15870 Zografou, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0308-4265","authenticated-orcid":false,"given":"Christos","family":"Makropoulos","sequence":"additional","affiliation":[{"name":"Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens (NTUA), 9 Heroon Polytechneiou St., 15870 Zografou, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1034","DOI":"10.1021\/ie50356a023","article-title":"Mass Transfer between Phases","volume":"31","author":"Sherwood","year":"1939","journal-title":"Ind. Eng. Chem."},{"key":"ref_2","unstructured":"Sherwood, T.K. (1959). Mass Transfer between Phases, Penn State University. Priestley Lecture, Phi Lambda Upsilon."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105232","DOI":"10.1016\/j.resconrec.2020.105232","article-title":"Evaluating economic opportunities for product recycling via the Sherwood principle and machine learning","volume":"167","author":"Deng","year":"2021","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.jenvman.2017.07.026","article-title":"Sewer-mining: A water reuse option supporting circular economy, public service provision and entrepreneurship","volume":"216","author":"Makropoulos","year":"2017","journal-title":"J. Environ. Manag."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liakopoulou, A., Makropoulos, C., Nikolopoulos, D., Monokrousou, K., and Karakatsanis, G. (2020). An Urban Water Simulation Model for the Design, Testing and Economic Viability Assessment of Distributed Water Management Systems for a Circular Economy. Environ. Sci. Proc., 2.","DOI":"10.3390\/environsciproc2020002014"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1086\/254195","article-title":"The Economics of Exhaustible Resources","volume":"39","author":"Hotelling","year":"1931","journal-title":"J. Political Econ."},{"key":"ref_7","unstructured":"United Nations (UN) (2022, November 25). System of Environmental Economic Accounting (SEEA) 2012: Central Framework. New York, USA, 2014, ISBN (UN): 987-92-1-161563-0. Available online: https:\/\/unstats.un.org\/unsd\/envaccounting\/seearev\/seea_cf_final_en.pdf."},{"key":"ref_8","unstructured":"World Commission on Environment and Development (1987). Our Common Future, Oxford University Press."},{"key":"ref_9","unstructured":"Official Journal of the European Communities (2022, December 17). Directive 2000\/60\/EC of the European Parliament and of the Council of October 2000; Establishing A Framework for Community Action in the Field of Water Policy, L 327\/1, Document 32000L0060. Available online: https:\/\/eur-lex.europa.eu\/legal-content\/EN\/TXT\/?uri=celex%3A32000L0060."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"7543","DOI":"10.1021\/es062254b","article-title":"What gets recycled: An information theory based model for product recycling","volume":"41","author":"Dahmus","year":"2007","journal-title":"Environ. Sci. Technol."},{"key":"ref_11","unstructured":"Gutowski, T.G., Wolf, M.I., Dahmus, J.B., and Albino, D.K. (2008., January 7\u201310). Analysis of Recycling Systems. Proceedings of the 2008 NSF Engineering Research and Innovation Conference, Knoxville, TE, USA. Available online: http:\/\/web.mit.edu\/ebm\/www\/Publications\/NSFJan08.pdf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"20428","DOI":"10.1073\/pnas.1012253108","article-title":"Economic and energetic analysis of capturing CO2 from ambient air","volume":"108","author":"House","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_13","unstructured":"National Academy of Engineering (1994). The Greening of Industrial Ecosystems, The National Academies Press."},{"key":"ref_14","unstructured":"Helmenstine, A.M. (2022, November 25). Learn about STP in Chemistry. ThoughtCo. Available online: thoughtco.com\/stp-in-chemistry-607533."},{"key":"ref_15","unstructured":"International Union of Pure and Applied Chemistry (IUPAC) (2007). Quantities, Units and Symbols in Physical Chemistry, RSC Publishing. [3rd ed.]. prepared by Cohen et al for the IUPAC Physical and Biophysical Chemistry Division."},{"key":"ref_16","unstructured":"International Union of Pure and Applied Chemistry (IUPAC) (1993). Quantities, Units and Symbols in Physical Chemistry, Blackwell Science. [2nd ed.]. Prepared by Mills et al. for the IUPAC Physical Chemistry Division."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1351\/pac199668040957","article-title":"Glossary of Terms in Quantities and Units in Clinical Chemistry (IUPAC-IFCC Recommendations 1996)","volume":"68","author":"Lehmann","year":"1996","journal-title":"Pure Appl. Chem."},{"key":"ref_18","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 Syst. Tech. J."},{"key":"ref_19","unstructured":"Baez, J.C. (2011). Renyi Entropy and Free Energy (v4). Quantum Physics (quant-ph). arXiv."},{"key":"ref_20","unstructured":"Karakatsanis, G., Mamassis, N., Koutsoyiannis, D., and Efstratiadis, A. Entropy and reliability of water use via a statistical approach of scarcity. Proceedings of the Facets of Uncertainty: 5th EGU Leonardo Conference\u2014Hydrofractals 2013\u2013STAHY 2013, EGU, IAHS and IUGG, Kos, Greece."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1162\/1088198041269472","article-title":"Applying ecological input-output flow analysis to material flows in industrial systems: Part I: Tracing flows","volume":"8","author":"Bailey","year":"1992","journal-title":"J. Ind. Ecol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0038-0121(89)90045-1","article-title":"Integrating Economic and Environmental Models: Some Preliminary Considerations","volume":"23","author":"Bolton","year":"1989","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_23","unstructured":"Capros, P. (1996). Integrated Economy\/Energy\/Environment Models, International Atomic Energy Agency (IAEA), International Nuclear Information System (INIS)."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0038-0121(79)90011-9","article-title":"A pollution theory of value","volume":"13","author":"Climis","year":"1979","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_25","unstructured":"International Energy Agency (IEA) (2022, November 25). A 10-Point Plan to Reduce the European Union\u2019s Reliance on Russian Natural Gas. Available online: https:\/\/iea.blob.core.windows.net\/assets\/1af70a5f-9059-47b4-a2dd-1b479918f3cb\/A10-PointPlantoReducetheEuropeanUnionsRelianceonRussianNaturalGas.pdf."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Croci, E. (2005). The Handbook of Environmental Voluntary Agreements, Environment & Policy; Springer.","DOI":"10.1007\/1-4020-3356-7"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.egypro.2017.08.073","article-title":"Energy, variability and weather finance engineering","volume":"125","author":"Karakatsanis","year":"2017","journal-title":"Energy Procedia"},{"key":"ref_28","unstructured":"Karakatsanis, G., Mamassis, N., Koutsoyiannis, D., and Efstratiadis, A. (2014). Entropy, Pricing and Macroeconomics of Pumped-Storage Systems, European Geosciences Union (EGU) General Assembly."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1016\/S1066-7938(02)00108-2","article-title":"Safe Companies: An Alternative Approach to Operationalizing Sustainability","volume":"9","author":"Gilding","year":"2002","journal-title":"Corp. Environ. Strategy"},{"key":"ref_30","first-page":"1","article-title":"Circular economy and innovation: A look from the perspective of organizational capabilities","volume":"31","author":"Sehnem","year":"2021","journal-title":"Bus. Strategy Environ."},{"key":"ref_31","unstructured":"Gr\u00fcbler, A. (2015). Technology and Global Change, Cambridge University Press."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0301-4207(76)90016-7","article-title":"Metal prices as a function of ore grade","volume":"2","author":"Phillips","year":"1976","journal-title":"Resource Policy"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0040-1625(86)90053-3","article-title":"A Critical Examination of the Ultimate Resource and the Resourceful Earth","volume":"30","author":"Trainer","year":"1986","journal-title":"Technol. Forecast. Soc. Change"},{"key":"ref_34","unstructured":"National Academies of Sciences, Engineering and Medicine (1987). Separation and Purification: Critical Needs and Opportunities, The National Academies Press."},{"key":"ref_35","unstructured":"Domenech, T., Doranova, A., Roman, L., Smith, M., and Artola, I. (2018). Cooperation Fostering Industrial Symbiosis: Market Potential, Good Practice and Policy Actions: Final Report, Publications Office."},{"key":"ref_36","unstructured":"European Commission (2019). Accelerating the Transition to the Circular Economy: Improving Access to Finance for Circular Economy Projects, Publications Office."},{"key":"ref_37","unstructured":"European Investment Bank (EIB) (2022, November 25). Circular Economy Overview 2021. Available online: https:\/\/www.eib.org\/attachments\/thematic\/circular_economy_overview_2021_en.pdf."},{"key":"ref_38","unstructured":"European Commission (2022, November 25). Financing a Sustainable European Economy. Final Report by the EU High-Level Expert Group on Sustainable Finance. Available online: https:\/\/ec.europa.eu\/info\/sites\/default\/files\/180131-sustainable-finance-final-report_en.pdf."},{"key":"ref_39","unstructured":"European Commission (2022, November 25). Circular Economy Action Plan for a Cleaner and More Competitive Europe. Available online: https:\/\/ec.europa.eu\/environment\/pdf\/circular-economy\/new_circular_economy_action_plan.pdf."},{"key":"ref_40","unstructured":"European Commission (2018). Report on Critical Raw Materials in the Circular Economy, Publications Office."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/j.ecolecon.2004.12.011","article-title":"How to compare companies on relevant dimensions of sustainability","volume":"55","author":"Krajnc","year":"2005","journal-title":"Ecol. Econ."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S1470-160X(01)00006-1","article-title":"Sustainability indices with multiple objectives","volume":"1","author":"Popp","year":"2001","journal-title":"Ecol. Indic."},{"key":"ref_43","unstructured":"Spangenberg, J.H., Femia, A., Hinterberger, F., Sch\u00fctz, H., Bringezu, S., Liedtke, C., and Schmidt-Bleek, F. (1998). Material Flow-based Indicators in Environmental Reporting, European Environment Agency (EEA)."},{"key":"ref_44","unstructured":"European Commission (2018). Final Report of the High-Level Panel of the European Decarbonisation Pathways Initiative, Publications Office."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.ecolecon.2006.02.012","article-title":"Economic and environmental efficiency using a social accounting matrix","volume":"60","author":"Morilla","year":"2006","journal-title":"Ecol. Econ."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0921-3449(04)00120-X","article-title":"A model for integrated assessment of sustainable development","volume":"43","author":"Krajnc","year":"2005","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_47","unstructured":"Organization of Economic Co-operation and Development (OECD) (2004). Measuring Sustainable Development: Integrated Economic, Environmental and Social Frameworks, OECD Publishing."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/S0954-349X(05)80004-9","article-title":"Environmental multipliers from a system of physical resource accounting","volume":"2","author":"Martin","year":"1991","journal-title":"Struct. Chang. Econ. Dyn."},{"key":"ref_49","unstructured":"Roussis, D., Karakatsanis, G., and Makropoulos, C. (2017, January 4\u20135). A macroeconomic model of water capital conservation. Proceedings of the 4th International Conference of Water Economics, Statistics and Finance, Livorno, Italy."},{"key":"ref_50","unstructured":"Walter, N., and Snyder, C. (2007). Microeconomic Theory: Basic Principles and Extensions, Thomson South-Western. [10th ed.]."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Georgescu-Roegen, N. (1971). The Entropy Law and the Economic Process, Harvard University Press.","DOI":"10.4159\/harvard.9780674281653"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3623","DOI":"10.1016\/j.enpol.2005.08.003","article-title":"Green energy strategies for sustainable development","volume":"34","author":"Midilli","year":"2006","journal-title":"Energy Policy"},{"key":"ref_53","unstructured":"Dasgupta, P., and M\u00e4ler, K.-G. (2022, November 25). Environmental and Resource Economics: Some Recent Developments. Available online: https:\/\/www.econ.cam.ac.uk\/people-files\/emeritus\/pd10000\/publications\/survey.pdf."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5751\/ES-01296-1001r03","article-title":"Integrating Methods for Developing Sustainability Indicators to Facilitate Learning and Action","volume":"10","author":"Reed","year":"2005","journal-title":"Ecol. Soc."},{"key":"ref_55","unstructured":"Hottel, C.H. (1994). Thomas Kilgore Sherwood 1903\u20131976: A Bibliographical Memoir, National Academy of Sciences. Available online: https:\/\/cart.nap.edu\/resource\/biomems\/tsherwood.pdf."},{"key":"ref_56","unstructured":"Conrad, K. (2001). Computable General Equilibrium Models in Environmental and Resource Economics, Institut f\u00fcr Volkswirtschaftslehre und Statistik, Abteilung f\u00fcr Volkswirtschaftslehre, University of Manheim. Discussion Papers 601."},{"key":"ref_57","unstructured":"Qi, F., Li, W.-H., Yu, S.-B., Du, X.-Y., and Guo, B.-N. (2019). A Ratio of Many Gamma Functions and its Properties with Applications (v1). Classical Analysis and ODEs (math.CA). arXiv."},{"key":"ref_58","unstructured":"Weisstein, E.W. (2022, November 25). Binomial Coefficient. From MathWorld\u2014A Wolfram Web Resource. Available online: https:\/\/mathworld.wolfram.com\/BinomialCoefficient.html."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"291","DOI":"10.2307\/2296305","article-title":"Production Functions with Constant Elasticities of Substitution","volume":"29","author":"Uzawa","year":"1962","journal-title":"Rev. Econ. Stud."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.egypro.2016.10.018","article-title":"Exergy and the economic process","volume":"97","author":"Karakatsanis","year":"2016","journal-title":"Energy Procedia"},{"key":"ref_61","unstructured":"Independent Power Transmission Operator (IPTO) (2022, November 25). System Marginal Price (SMP) vs. Clearances Marginal Price (CMP) Data, November 2019\u2014October 2020. Available online: https:\/\/www.admie.gr\/en\/market\/market-statistics\/key-data\/sip-vs-smp."},{"key":"ref_62","unstructured":"Kontarakis, E., Karakatsanis, G., Dimitriadis, P., Iliopoulou, T., and Koutsoyiannis, D. (2018). Hydroclimate and Agricultural Output in Developing Countries, European Geosciences Union (EGU) General Assembly."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1073\/pnas.89.3.879","article-title":"Industrial ecology: Reflections on a colloquium","volume":"89","author":"Ausubel","year":"1992","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/0959-6526(95)00045-G","article-title":"Industrial ecology and industrial ecosystems","volume":"3","author":"Lowe","year":"1995","journal-title":"J. Clean. Prod."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.techsoc.2004.01.013","article-title":"Industrial ecology: A teenager\u2019s progress","volume":"26","author":"Harper","year":"2004","journal-title":"Technol. Soc."},{"key":"ref_66","first-page":"89","article-title":"Industrial Ecology: A Critical Review","volume":"6","author":"Connelly","year":"1996","journal-title":"Int. J. Environ. Pollut."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1504\/PIE.2006.010039","article-title":"The ontologies of industrial ecology?","volume":"3","author":"Brad","year":"2006","journal-title":"Prog. Ind. Ecol. Int. J."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"83","DOI":"10.3197\/0963271053306096","article-title":"Industrial Ecology for Sustainable Development: Six Controversies in Theory Building","volume":"14","author":"Jouni","year":"2005","journal-title":"Environ. Values"},{"key":"ref_69","unstructured":"Karakatsanis, G., Mamassis, N., Koutsoyiannis, A., and Efstratiadis, A. (2014). Entropy, Recycling and Macroeconomics of Water Resources, European Geosciences Union (EGU) General Assembly."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"1686","DOI":"10.1021\/ed083p1686","article-title":"Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property","volume":"83","author":"Jungermann","year":"2006","journal-title":"J. Chem. Educ."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1016\/0016-3287(94)90071-X","article-title":"Technology and the Transition to Environmental Sustainability: The problem of technological regime shifts","volume":"26","author":"Rene","year":"1994","journal-title":"Futures"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Schaltegger, S., Bennett, M., and Burritt, R. (2006). Sustainability Accounting and Reporting, Springer.","DOI":"10.1007\/978-1-4020-4974-3"},{"key":"ref_73","first-page":"9","article-title":"Chemical leasing in the context of sustainable chemistry","volume":"22","author":"Frank","year":"2014","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0304-4076(74)90034-7","article-title":"Spurious Regressions in Econometrics","volume":"2","author":"Granger","year":"1974","journal-title":"J. Econom."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:44:38Z","timestamp":1760147078000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,20]]},"references-count":74,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010004"],"URL":"https:\/\/doi.org\/10.3390\/e25010004","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,20]]}}}