{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T05:33:27Z","timestamp":1777354407623,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T00:00:00Z","timestamp":1539907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.<\/jats:p>","DOI":"10.3390\/e20100804","type":"journal-article","created":{"date-parts":[[2018,10,19]],"date-time":"2018-10-19T10:08:02Z","timestamp":1539943682000},"page":"804","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Group Entropies: From Phase Space Geometry to Entropy Functionals via Group Theory"],"prefix":"10.3390","volume":"20","author":[{"given":"Henrik","family":"Jeldtoft Jensen","sequence":"first","affiliation":[{"name":"Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK"},{"name":"Institute of Innovative Research, Tokyo Institute of Technology, 4259, Nagatsuta-cho, Yokohama 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5186-2378","authenticated-orcid":false,"given":"Piergiulio","family":"Tempesta","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, Universidad Complutense de Madrid, 28040 Madrid, Spain"},{"name":"Instituto de Ciencias Matem\u00e1ticas (ICMAT), 28049 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20160143","DOI":"10.1098\/rspa.2016.0143","article-title":"Formal groups and Z-entropies","volume":"472","author":"Tempesta","year":"2016","journal-title":"Proc. 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