{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T04:15:53Z","timestamp":1781842553660,"version":"3.54.5"},"reference-count":110,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,12]],"date-time":"2019-01-12T00:00:00Z","timestamp":1547251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["1643433"],"award-info":[{"award-number":["1643433"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["RP2013-SL-015"],"award-info":[{"award-number":["RP2013-SL-015"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Since its conception over 150 years ago, entropy has enlightened and confused scholars and students alike, from its origins in physics and beyond. More recently, it has been considered within the urban context in a rather eclectic range of applications. The entropy maximization approach, as applied by Alan Wilson and others from the 1960s, contrasts with considerations from the 1990s of the city as a thermodynamic dissipative system, in the tradition of Ilya Prigogine. By reviewing the relevant mathematical theory, we draw the distinction among three interrelated definitions of entropy, the thermodynamic, the figurative, and the information statistical. The applications of these definitions to urban systems within the literature are explored, and the conflation of the thermodynamic and figurative interpretations are disentangled. We close this paper with an outlook on future uses of entropy in urban systems analysis.<\/jats:p>","DOI":"10.3390\/e21010056","type":"journal-article","created":{"date-parts":[[2019,1,14]],"date-time":"2019-01-14T12:20:07Z","timestamp":1547468407000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":57,"title":["Entropy and its Application to Urban Systems"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8883-5472","authenticated-orcid":false,"given":"Ben","family":"Purvis","sequence":"first","affiliation":[{"name":"Laboratory for Urban Complexity and Sustainability, University of Nottingham, Nottingham NG7 2RD, UK"},{"name":"School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2317-1171","authenticated-orcid":false,"given":"Yong","family":"Mao","sequence":"additional","affiliation":[{"name":"Laboratory for Urban Complexity and Sustainability, University of Nottingham, Nottingham NG7 2RD, UK"},{"name":"School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Darren","family":"Robinson","sequence":"additional","affiliation":[{"name":"Laboratory for Urban Complexity and Sustainability, University of Nottingham, Nottingham NG7 2RD, UK"},{"name":"School of Architecture, University of Sheffield, Sheffield S10 2TN, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,12]]},"reference":[{"key":"ref_1","unstructured":"(2018, October 26). Oxford Dictionaries. Available online: https:\/\/en.oxforddictionaries.com\/definition\/entropy."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information Theory and Statistical Mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1088\/0305-4470\/25\/4\/038","article-title":"Generalized statistical mechanics: Connection with thermodynamics","volume":"25","author":"Curado","year":"1992","journal-title":"J. Phys. A. Math. Gen."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/PhysRevLett.117.260601","article-title":"Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies","volume":"117","author":"Weilenmann","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nphys3230","article-title":"Thermodynamics of information","volume":"11","author":"Parrondo","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","article-title":"Information Theory and Statistical Mechanics. II","volume":"108","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/0304-4009(76)90004-8","article-title":"The city system and the use of entropy in urban analysis","volume":"2","author":"Ayeni","year":"1976","journal-title":"Urban Ecol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Batty, M. (2008). Cities as Complex Systems: Scaling, Interactions, Networks, Dynamics and Urban Morphologies. The Encyclopedia of Complexity & System Science, Springer.","DOI":"10.1007\/978-0-387-30440-3_69"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1080\/01944369408975547","article-title":"Operational Urban Models State of the Art","volume":"60","author":"Wegener","year":"1994","journal-title":"J. Am. Plan. Assoc."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Robinson, D. (2011). Computer Modelling for Sustainable Urban Design, Routledge.","DOI":"10.4324\/9781849775403"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10708-013-9516-8","article-title":"The real-time city? Big data and smart urbanism","volume":"79","author":"Kitchin","year":"2014","journal-title":"GeoJournal"},{"key":"#cr-split#-ref_12.1","unstructured":"UN (2015). Transforming Our World: The 2030 Agenda for Sustainable Development"},{"key":"#cr-split#-ref_12.2","unstructured":"Resolution Adopted by the General Assembly on 25 September 2015 (A\/RES\/70\/1), United Nations."},{"key":"ref_13","unstructured":"Rees, W., and Wackernagel, M. (1997). Urban Ecological Footprints: Why Cities Cannot be Sustainable\u2014And Why They are a Key to Sustainability. Urban Ecology, Springer."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"222","DOI":"10.2495\/ECO-V2-N4-222-230","article-title":"Quo vadis thermodynamics and the city: A critical review of applications of thermodynamic methods to urban systems","volume":"2","author":"Filchakova","year":"2007","journal-title":"Int. J. Ecodynamics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/jiec.12239","article-title":"Why Do Cities Grow? Insights from Nonequilibrium Thermodynamics at the Urban and Global Scales","volume":"19","author":"Bristow","year":"2015","journal-title":"J. Ind. Ecol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1002\/adic.200690056","article-title":"Non Equilibrium Thermodynamics and the City: A New Approach to Urban Studies","volume":"96","author":"Pulselli","year":"2006","journal-title":"Ann. Chim."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1016\/j.enpol.2005.04.022","article-title":"Sustainability and information in urban system analysis","volume":"34","author":"Balocco","year":"2006","journal-title":"Energy Policy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"537","DOI":"10.2495\/SC140451","article-title":"The Sustainable City and the Smart City: Measuring urban entropy first","volume":"191","author":"Fistola","year":"2014","journal-title":"Trans. Ecol. Environ."},{"key":"ref_19","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_20","unstructured":"Nicolis, G., and Prigogine, I. (1977). Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations, Wiley. A Wiley-Interscience Publication."},{"key":"ref_21","unstructured":"Wilson, A.G. (1970). Entropy in Urban and Regional Modelling, Pion."},{"key":"ref_22","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_23","first-page":"40","article-title":"A Primer on Entropy Modeling","volume":"41","author":"Cesario","year":"1975","journal-title":"J. Am. Plan. Assoc."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"De Martino, A., and De Martino, D. (2018). An introduction to the maximum entropy approach and its application to inference problems in biology. Heliyon, 4.","DOI":"10.1016\/j.heliyon.2018.e00596"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Lesne, A. (2014). Shannon entropy: A rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics. Math. Struct. Comput. Sci., 24.","DOI":"10.1017\/S0960129512000783"},{"key":"ref_26","first-page":"646","article-title":"Maximum entropy method in image processing","volume":"131","author":"Gull","year":"1984","journal-title":"IEE Proc. F"},{"key":"ref_27","unstructured":"Kondepudi, D.K. (2008). Introduction to Modern Thermodynamics, Wiley."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2008). Entropy Demystified: The Second Law Reduced to Plain Common Sense, World Scientific.","DOI":"10.1142\/6916"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Goold, J., Huber, M., Riera, A., Del Rio, L., and Skrzypczyk, P. (2016). The role of quantum information in thermodynamics - A topical review. J. Phys. A Math. Theor., 49.","DOI":"10.1088\/1751-8113\/49\/14\/143001"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"317","DOI":"10.2307\/143147","article-title":"The Application of Information Theory to the Analysis of Population Distributions in Space","volume":"46","author":"Chapman","year":"1970","journal-title":"Econ. Geogr."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"523","DOI":"10.2747\/0272-3638.10.6.523","article-title":"The Most Ethnically Diverse Urban Places in the United States","volume":"10","author":"Allen","year":"1989","journal-title":"Urban Geogr."},{"key":"ref_32","first-page":"83","article-title":"Measurement and monitoring of urban sprawl in a rapidly growing region using entropy","volume":"67","author":"Yeh","year":"2001","journal-title":"Photogramm. Eng. Remote Sensing"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"5223","DOI":"10.3390\/e15125223","article-title":"Entropy in Urban Systems","volume":"15","author":"Cabral","year":"2013","journal-title":"Entropy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1111\/j.1467-9531.2011.01237.x","article-title":"Entropy-based segregation indices","volume":"41","author":"Mora","year":"2011","journal-title":"Sociol. Methodol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1068\/a090395","article-title":"Information theory: Some concepts and measures","volume":"9","author":"Walsh","year":"1977","journal-title":"Environ. Plan. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.ecolmodel.2005.03.026","article-title":"Maximum entropy modeling of species geographic distributions","volume":"190","author":"Phillips","year":"2006","journal-title":"Ecol. Model."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1109\/JSTARS.2010.2084072","article-title":"Monitoring Urban Sprawl Using Remote Sensing and GIS Techniques of a Fast Growing Urban Centre, India","volume":"4","author":"Rahman","year":"2011","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"486","DOI":"10.4028\/www.scientific.net\/AMM.225.486","article-title":"Remote Sensing Data Derived Parameters and its Use in Landslide Susceptibility Assessment Using Shannon\u2019s Entropy and GIS","volume":"225","author":"Pourghasemi","year":"2012","journal-title":"Appl. Mech. Mater."},{"key":"ref_39","first-page":"26","article-title":"Monitoring and modelling of urban sprawl using remote sensing and GIS techniques","volume":"10","author":"Jat","year":"2008","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_40","first-page":"29","article-title":"Urban sprawl: Metrics, dynamics and modelling using GIS","volume":"5","author":"Sudhira","year":"2004","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Li, L., Xing, X., Xia, H., and Huang, X. (2016). Entropy-Weighted instance matching between different sourcing points of interest. Entropy, 18.","DOI":"10.3390\/e18020045"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1111\/j.1435-5597.1967.tb01362.x","article-title":"The Concept of Entropy in Settlement Pattern Analysis","volume":"18","author":"Medvedkov","year":"1967","journal-title":"Pap. Reg. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1538-4632.1976.tb00525.x","article-title":"Entropy in Spatial Aggregation","volume":"8","author":"Batty","year":"1976","journal-title":"Geogr. Anal."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1007\/s10109-014-0202-2","article-title":"Entropy, complexity, and spatial information","volume":"16","author":"Batty","year":"2014","journal-title":"J. Geogr. Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1538-4632.1974.tb01014.x","article-title":"Spatial Entropy","volume":"6","author":"Batty","year":"1974","journal-title":"Geogr. Anal."},{"key":"ref_46","unstructured":"Theil, H. (1967). Economics and Information Theory, North-Holland Pub. Co."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/0040-5809(82)90004-1","article-title":"Diversity and Dissimilarity","volume":"21","author":"Rao","year":"1982","journal-title":"Theor. Popul. Biol."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0041-1647(67)90035-4","article-title":"A statistical theory of spatial distribution models","volume":"1","author":"Wilson","year":"1967","journal-title":"Transp. Res."},{"key":"ref_49","first-page":"108","article-title":"The Use of Entropy Maximising Models in the Theory of Trip Distribution, Mode Split and Route Split","volume":"3","author":"Wilson","year":"1969","journal-title":"J. Transp. Econ. Policy"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1111\/j.1538-4632.2010.00799.x","article-title":"Entropy in urban and regional modelling: Retrospect and prospect","volume":"42","author":"Wilson","year":"2010","journal-title":"Geogr. Anal."},{"key":"ref_51","first-page":"536","article-title":"Science and Complexity","volume":"36","author":"Weaver","year":"1948","journal-title":"Am. Sci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1068\/a100185","article-title":"Reilly\u2019s challenge: New laws of retail gravitation which define systems of central places","volume":"10","author":"Batty","year":"1978","journal-title":"Environ. Plan. A"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1177\/030913257900300218","article-title":"From gravity modelling entropy maximizing: A pedagogic guide","volume":"3","author":"Senior","year":"1979","journal-title":"Prog. Hum. Geogr."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1057\/jors.1970.48","article-title":"The Use of the Concept of Entropy in System Modelling","volume":"21","author":"Wilson","year":"1970","journal-title":"Oper. Res. Q."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1080\/03081067308717045","article-title":"Further developments of entropy maximising transport models","volume":"1","author":"Wilson","year":"1973","journal-title":"Transp. Plan. Technol."},{"key":"ref_56","unstructured":"Angel, S., and Hyman, G.M. (1976). Urban Fields: A Geometry of Movement for Regional Science, Pion."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1080\/0020739820130604","article-title":"Entropy maximization models in regional and urban planning","volume":"13","author":"Kapur","year":"1982","journal-title":"Int. J. Math. Educ. Sci. Technol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/0166-0462(77)90021-7","article-title":"A Minimum Information Principle: Theory and Practice","volume":"7","author":"Snickars","year":"1977","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0191-2615(80)90008-9","article-title":"The Most Likely Trip Matrix Estimated from Traffic Counts","volume":"14","author":"Willumsen","year":"1980","journal-title":"Transp. Res. Part B"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0191-2615(88)90024-0","article-title":"A unified framework for estimating or updating origin\/destination matrices from traffic counts","volume":"22","author":"Cascetta","year":"1988","journal-title":"Transp. Res. Part B"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1068\/a120187","article-title":"Explorations into the relationship between spatial structure and spatial interaction","volume":"12","author":"Griffith","year":"1980","journal-title":"Environ. Plan. A"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0166-0462(84)90021-8","article-title":"Equivalence Between Welfare and Entropy Approaches to Residential Location","volume":"14","author":"Mattsson","year":"1984","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0191-2615(81)90035-7","article-title":"On appropriate microstate descriptions in entropy modelling","volume":"15","author":"Roy","year":"1981","journal-title":"Transp. Res. Part B"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"116","DOI":"10.3390\/e3030116","article-title":"Energy, Entropy and Exergy Concepts and Their Roles in Thermal Engineering Ibrahim","volume":"3","author":"Dincer","year":"2001","journal-title":"Entropy"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1243\/0957650011538424","article-title":"Exergy analysis of the United Kingdom energy system","volume":"215","author":"Hammond","year":"2001","journal-title":"Proc. Inst. Mech. Eng. Part A J. Power Energy"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.ecolecon.2003.08.006","article-title":"Using exergy to analyze the sustainability of an urban area","volume":"48","author":"Balocco","year":"2004","journal-title":"Ecol. Econ."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0038-092X(00)00069-4","article-title":"Thermodynamic parameters for energy sustainability of urban areas","volume":"69","author":"Balocco","year":"2000","journal-title":"Sol. Energy"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jclepro.2014.08.035","article-title":"Sustainability analysis of a society based on exergy studies\u2014A case study of the island of Sams\u00f8 (Denmark)","volume":"96","author":"Nielsen","year":"2015","journal-title":"J. Clean. Prod."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"2492","DOI":"10.1016\/j.ijhydene.2016.02.048","article-title":"Energy and exergy analyses of a hybrid hydrogen energy system: A case study for Bozcaada","volume":"42","author":"Kalinci","year":"2017","journal-title":"Int. J. Hydrogen Energy"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1177\/0306419016689501","article-title":"Demystification of the Gouy-Stodola theorem of thermodynamics for closed systems","volume":"45","author":"Pal","year":"2017","journal-title":"Int. J. Mech. Eng. Educ."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1063\/1.362674","article-title":"Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes","volume":"79","author":"Bejan","year":"1996","journal-title":"J. Appl. Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s13369-012-0444-6","article-title":"Entropy generation minimization, exergy analysis, and the constructal law","volume":"38","author":"Bejan","year":"2013","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1016\/j.proeng.2017.07.131","article-title":"Thermodynamic Entropy as an Indicator for Urban Sustainability?","volume":"198","author":"Purvis","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_74","first-page":"1","article-title":"A brief Commented History of Exergy from the Beginnings to 2004","volume":"10","author":"Sciubba","year":"2007","journal-title":"Int. J. Thermodyn."},{"key":"ref_75","unstructured":"Kotas, T.J. (1985). The Exergy Method of Thermal Plant Analysis, Butterworths."},{"key":"ref_76","first-page":"263","article-title":"Entropy and the city","volume":"93","author":"Marchettini","year":"2006","journal-title":"WIT Trans. Ecol. Environ."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Rees, W.E. (2012). Cities as Dissipative Structures: Global Change and the Vulnerability of Urban Civilization. Sustainability Science: The Emerging Paradigm and the Urban Environment, Springer.","DOI":"10.1007\/978-1-4614-3188-6_12"},{"key":"ref_78","unstructured":"Lovelock, J. (1979). Gaia, a New Look at Life on Earth, Oxford University Press."},{"key":"ref_79","unstructured":"Rifkin, J., and Howard, T. (1980). Entropy: A New World View, Viking Press."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.proeng.2011.11.2102","article-title":"The unsustainable city. Urban entropy and social capital: The needing of a new urban planning","volume":"21","author":"Fistola","year":"2011","journal-title":"Procedia Eng."},{"key":"ref_81","first-page":"195","article-title":"Urban entropy vs sustainability: A new town planning perspective","volume":"155","author":"Fistola","year":"2012","journal-title":"Sustain. City"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.landurbplan.2017.10.002","article-title":"The low-entropy city: A thermodynamic approach to reconnect urban systems with nature","volume":"168","author":"Pelorosso","year":"2017","journal-title":"Landsc. Urban Plan."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.energy.2016.01.071","article-title":"Misuse of thermodynamic entropy in economics","volume":"100","author":"Kovalev","year":"2016","journal-title":"Energy"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.ecolecon.2004.12.020","article-title":"Entropy and its misuse, I. Energy, free and otherwise","volume":"56","author":"Gillett","year":"2006","journal-title":"Ecol. Econ."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1521\/siso.2007.72.1.43","article-title":"The Limits to Entropy: The Continuing Misuse of Thermodynamics in Environmental and Marxist theory","volume":"72","author":"Schwartzman","year":"2008","journal-title":"Sci. Soc."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF01175750","article-title":"The balance of entropy on earth","volume":"8","author":"Weiss","year":"1994","journal-title":"Contin. Mech. Thermodyn. Anal. Complex Mater. Judicious Eval. Environ."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1021\/ed079p187","article-title":"Disorder\u2014A Cracked Crutch for Supporting Entropy Discussions","volume":"79","author":"Lambert","year":"2002","journal-title":"J. Chem. Educ."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s11191-017-9892-4","article-title":"Good Use of a \u201cBad\u201d Metaphor: Entropy as Disorder","volume":"26","author":"Haglund","year":"2017","journal-title":"Sci. Educ."},{"key":"ref_89","first-page":"3","article-title":"The Entropy Law and The Economic Process in Retrospect","volume":"12","year":"1986","journal-title":"East. Econ. J."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/S0921-8009(00)00225-1","article-title":"Entropy and economic processes\u2014Physics perspectives","volume":"36","year":"2001","journal-title":"Ecol. Econ."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1111\/j.1749-6632.2009.05166.x","article-title":"Connecting thermodynamics and economics: Well-lit roads and burned bridges","volume":"1185","author":"Glucina","year":"2010","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"ref_92","unstructured":"Szenberg, M. (1992). Nicholas Georgescu-Roegen about Himself. Eminent Economists: Their Life Philosophies, Cambridge University Press."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1108\/03068290910932756","article-title":"Georgescu-Roegen\u2019s entropic model: A methodological appraisal","volume":"36","author":"Cojanu","year":"2009","journal-title":"Int. J. Soc. Econ."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.ecolecon.2004.02.012","article-title":"The early history of modern ecological economics","volume":"50","year":"2004","journal-title":"Ecol. Econ."},{"key":"ref_95","unstructured":"Wright, J.D. (2015). Ecological economics. International Encyclopedia of the Social & Behavioral Sciences, Elsevier. [2nd ed.]."},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"2271","DOI":"10.1016\/j.ecolecon.2010.06.020","article-title":"Can de-growth be considered a policy option? A historical note on Nicholas Georgescu-Roegen and the Club of Rome","volume":"69","author":"Levallois","year":"2010","journal-title":"Ecol. Econ."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1038\/scientificamerican0965-178","article-title":"The Metabolism of Cities","volume":"213","author":"Wolman","year":"1965","journal-title":"Sci. Am."},{"key":"ref_98","unstructured":"Schr\u00f6dinger, E. (1944). What Is Life?, Cambridge University Press."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/0016-3287(94)90034-5","article-title":"Complexity and thermodynamics. Towards a new ecology","volume":"26","author":"Schneider","year":"1994","journal-title":"Futures"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0304-3800(97)00156-7","article-title":"State-of-the-art in ecosystem theory","volume":"100","year":"1997","journal-title":"Ecol. Model."},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Jorgensen, S.E., and Svirezhev, Y.M. (2004). Towards a Thermodynamic Theory for Ecological Systems, Elsevier.","DOI":"10.1016\/B978-008044166-5\/50009-4"},{"key":"ref_102","doi-asserted-by":"crossref","unstructured":"Hernando, A., and Plastino, A. (2012). Thermodynamics of urban population flows. Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 86.","DOI":"10.1103\/PhysRevE.86.066105"},{"key":"ref_103","unstructured":"Reggiani, A., and Nijkamp, P. (2009). The \u201cThermodynamics\u201d of the City: Evolution and Complexity Science in Urban Modelling. Complexity and Spatial Networks: In Search of Simplicity, Springer."},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"8980","DOI":"10.3390\/su6128980","article-title":"An entropy-perspective study on the sustainable development potential of tourism destination ecosystem in Dunhuang, China","volume":"6","author":"Feng","year":"2014","journal-title":"Sustainability"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ecolmodel.2006.02.032","article-title":"Analyses of urban ecosystem based on information entropy","volume":"197","author":"Zhang","year":"2006","journal-title":"Ecol. Model."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Ben-Naim, A. (2008). A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific.","DOI":"10.1142\/9789812790736"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1142\/S0218488503002089","article-title":"Conditional and Weighted Measures of Ecological Diversity","volume":"11","year":"2003","journal-title":"Int. J. Uncertain. Fuzziness Knowl.-Based Syst."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/0041-1647(75)90054-4","article-title":"Some new forms of spatial interaction model: A review","volume":"9","author":"Wilson","year":"1975","journal-title":"Transp. Res."},{"key":"ref_109","doi-asserted-by":"crossref","unstructured":"Clarke, G.P., and Wilson, A. (2009). International Encyclopedia of Human Geography, Elsevier.","DOI":"10.1016\/B978-008044910-4.00653-2"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/56\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:25:27Z","timestamp":1760185527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/56"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,12]]},"references-count":110,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["e21010056"],"URL":"https:\/\/doi.org\/10.3390\/e21010056","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,12]]}}}