{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T05:58:13Z","timestamp":1773295093960,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T00:00:00Z","timestamp":1597017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012550","name":"Nemzeti Kutat\u00e1si, Fejleszt\u00e9si \u00e9s Innovaci\u00f3s Alap","doi-asserted-by":"publisher","award":["K 123815"],"award-info":[{"award-number":["K 123815"]}],"id":[{"id":"10.13039\/501100012550","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006595","name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","doi-asserted-by":"publisher","award":["PN-III-P4-IID-PCCF-2016-0084"],"award-info":[{"award-number":["PN-III-P4-IID-PCCF-2016-0084"]}],"id":[{"id":"10.13039\/501100006595","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs\u2013Boltzmann\u2013Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.<\/jats:p>","DOI":"10.3390\/e22080879","type":"journal-article","created":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T09:28:57Z","timestamp":1597138137000},"page":"879","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Gintropy: Gini Index Based Generalization of Entropy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6188-8478","authenticated-orcid":false,"given":"Tam\u00e1s S.","family":"Bir\u00f3","sequence":"first","affiliation":[{"name":"Wigner Research Centre for Physics, 1121 Budapest, Hungary"},{"name":"Complexity Science Hub, 1080 Vienna, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7319-5123","authenticated-orcid":false,"given":"Zolt\u00e1n","family":"N\u00e9da","sequence":"additional","affiliation":[{"name":"Department of Physics, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"032124","DOI":"10.1103\/PhysRevE.96.032124","article-title":"The three faces of entropy for complex systems- information, thermodynamics and the maxent principle","volume":"96","author":"Thurner","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_2","unstructured":"Amigo, J., Balogh, S., and Hernandez, S. (2020). A Brief review of Generalized Entropies. Entropy, 22."},{"key":"ref_3","first-page":"1203","article-title":"Sulla misura della concentrazione e della variabilit\u00e1 dei caratteri","volume":"73","author":"Gini","year":"1914","journal-title":"Lettere Arti"},{"key":"ref_4","first-page":"209","article-title":"Methods of measuring the concentration of wealth","volume":"9","author":"Lorenz","year":"1905","journal-title":"Publ. Am. Stat. Assoc."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Marmani, S., Ficcadenti, V., Kaur, P., and Dhesi, G. (2020). Entropic Analysis of Votes Expressed in Italian Elections between 1948 and 2018. Entropy, 22.","DOI":"10.3390\/e22050523"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/0022-0531(70)90039-6","article-title":"On the measurement of inequality","volume":"2","author":"Atkinson","year":"1970","journal-title":"J. Econ. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"613","DOI":"10.2307\/1913126","article-title":"The Class of Additivity Decomposable Inequality Measures","volume":"48","author":"Shorrocks","year":"1980","journal-title":"Econometrica"},{"key":"ref_8","first-page":"750","article-title":"Cours d\u2019 economie politique","volume":"11","author":"Pareto","year":"1896","journal-title":"Political Sci. Q."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1086\/250454","article-title":"The New Theories of economics","volume":"5","author":"Pareto","year":"1897","journal-title":"J. Political Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"147","DOI":"10.2307\/1883096","article-title":"Vilfredo Pareto (1848\u20131923)","volume":"63","author":"Schumpeter","year":"1949","journal-title":"Q. J. Econ."},{"key":"ref_11","first-page":"140","article-title":"The Pareto Principle","volume":"7","author":"Dunford","year":"2014","journal-title":"Plymouth Stud. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/S0378-4371(97)00217-3","article-title":"New evidence for the power-law distribution of wealth","volume":"242","author":"Levy","year":"1997","journal-title":"Physica A"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Piketty, I. (2014). Capital in the Twenty-First, Century, Harvard University Press.","DOI":"10.4159\/9780674369542"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.physa.2005.02.092","article-title":"Evidence for the Power-law tail of the wealth-distribution in India","volume":"359","author":"Sinha","year":"2006","journal-title":"Physica A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1007\/s100510070114","article-title":"Statistical mechanics of money","volume":"17","author":"Dragulescu","year":"2000","journal-title":"Eur. Phys. J. B"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0378-4371(01)00298-9","article-title":"Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States","volume":"299","author":"Dragulescu","year":"2001","journal-title":"Physica A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"124491","DOI":"10.1016\/j.physa.2020.124491","article-title":"Scaling in income inequalities and its dynamical origin","volume":"549","author":"Neda","year":"2020","journal-title":"Physica A"},{"key":"ref_18","unstructured":"Molala, R. (2020, May 12). Entropy, Information Gain, Gini Index\u2014The Crux of a Decision Tree. Available online: https:\/\/blog.clairvoyantsoft.com."},{"key":"ref_19","first-page":"9","article-title":"Duality between the Lorenz curves and the income distribution functions","volume":"34","author":"Iritani","year":"1983","journal-title":"Econ. Stud. Q."},{"key":"ref_20","first-page":"183","article-title":"Duality between generalized Lorenz curves and distribution functions","volume":"40","author":"Thistle","year":"1989","journal-title":"Econ. Stud. Q."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1007\/s003550000046","article-title":"Characterizations of Lorenz curves and income distributions","volume":"17","author":"Aaberge","year":"2000","journal-title":"Soc. Choice Welf."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Betti, G., and Lemmi, A. (2008). The Lorenz curve in economics and econometrics. Advances on Income Inequality and Concentration Measures, Proceedings of the Gini-Lorenz Centennial Conference, Siena, Italy, 23\u201326 May 2005, Routledge. Collected Papers in Memory of Corrado Gini and Max O. Lorenz.","DOI":"10.4324\/9780203927922"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.physa.2018.02.078","article-title":"Unidirectional random growth with resetting","volume":"499","year":"2018","journal-title":"Physica A"},{"key":"ref_24","first-page":"413","article-title":"A new model of personal income distributiuons: Specification and estimation","volume":"30","author":"Dogum","year":"1977","journal-title":"Econ. Appliqu\u00e9e"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"647","DOI":"10.2307\/1913469","article-title":"Some generalized functions for the size distribution of income","volume":"52","author":"McDonald","year":"1984","journal-title":"Econometrica"},{"key":"ref_27","first-page":"181","article-title":"Lorenz ordering within the generalized gamma family of income distributions","volume":"6","author":"Taillie","year":"1981","journal-title":"Stat. Distrib. Sci. Work"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0165-1765(93)90134-X","article-title":"Lorenz ordering of Singh-Maddala income distributions","volume":"43","author":"Wilfling","year":"1993","journal-title":"Econ. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/S0378-4371(00)00205-3","article-title":"Wealth condensation in a simple model of economy","volume":"282","author":"Bouchaud","year":"2000","journal-title":"Physica A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1007\/s003550200154","article-title":"A characterization of income distributions in terms of generalized Gini coefficients","volume":"19","author":"Kleiber","year":"2002","journal-title":"Soc. Choice Welf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"617","DOI":"10.2307\/2648789","article-title":"On an extension of the Gini inequality index","volume":"24","author":"Yitzhaki","year":"1983","journal-title":"Int. Econ. Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/8\/879\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:58:52Z","timestamp":1760176732000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/8\/879"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,10]]},"references-count":31,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2020,8]]}},"alternative-id":["e22080879"],"URL":"https:\/\/doi.org\/10.3390\/e22080879","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,10]]}}}