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Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form.<\/jats:p>","DOI":"10.3390\/e26030266","type":"journal-article","created":{"date-parts":[[2024,3,18]],"date-time":"2024-03-18T06:58:39Z","timestamp":1710745119000},"page":"266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Group Structure as a Foundation for Entropies"],"prefix":"10.3390","volume":"26","author":[{"given":"Henrik Jeldtoft","family":"Jensen","sequence":"first","affiliation":[{"name":"Centre for Complexity Science and Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK"},{"name":"Department of Computer Science, School of Computing, 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 Fisica 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":[[2024,3,18]]},"reference":[{"key":"ref_1","unstructured":"Reif, F. 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