{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:15:32Z","timestamp":1761218132905,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,6]],"date-time":"2019-03-06T00:00:00Z","timestamp":1551830400000},"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 goal of this comment note is to express our considerations about the recent paper by A. Ben Naim (Entropy 2017, 19, 48). We strongly support the distinguishing between the Shannon measure of information and the thermodynamic entropy, suggested in the paper. We demonstrate that the Voronoi entropy should also be clearly distinguished from the entropy of a two-dimensional gas. Actually, the Voronoi entropy being an intensive value is the averaged Shannon measure of ordering for a given pattern.<\/jats:p>","DOI":"10.3390\/e21030251","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T10:52:22Z","timestamp":1551955942000},"page":"251","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Is the Voronoi Entropy a True Entropy? Comments on \u201cEntropy, Shannon\u2019s Measure of Information and Boltzmann\u2019s H-Theorem\u201d, Entropy 2017, 19, 48"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1356-2486","authenticated-orcid":false,"given":"Edward","family":"Bormashenko","sequence":"first","affiliation":[{"name":"Engineering Faculty, Chemical Engineering, Biotechnology and Materials Department, Ariel University, P.O.B. 3, 407000 Ariel, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"Frenkel","sequence":"additional","affiliation":[{"name":"Engineering Faculty, Chemical Engineering, Biotechnology and Materials Department, Ariel University, P.O.B. 3, 407000 Ariel, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6384-7570","authenticated-orcid":false,"given":"Irina","family":"Legchenkova","sequence":"additional","affiliation":[{"name":"Engineering Faculty, Chemical Engineering, Biotechnology and Materials Department, Ariel University, P.O.B. 3, 407000 Ariel, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ben Naim, A. 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Recherches sur les parall\u00e9lo\u00e8dres primitifs","volume":"134","author":"Voronoi","year":"1908","journal-title":"Reine Angew. Math."},{"key":"ref_6","unstructured":"Descartes, R. (1644). Principia Philosophiae, Ludovicus Elzevirius."},{"key":"ref_7","first-page":"419","article-title":"Voronoi diagrams and Delaunay triangulations: Ubiquitous Siamese Twins","volume":"ISMP","author":"Liebling","year":"2012","journal-title":"Doc. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2010.11.002","article-title":"Spatial networks","volume":"499","year":"2011","journal-title":"Phys. Rep."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Bormashenko, E., Frenkel, M., Vilk, A., Legchenkova, I., Fedorets, A., Aktaev, N., Dombrovsky, L., and Nosonovsky, M. (2018). Characterization of self-assembled 2D patterns with Voronoi Entropy. Entropy, 20.","DOI":"10.20944\/preprints201811.0535.v1"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5599","DOI":"10.1021\/acs.jpclett.7b02657","article-title":"Small levitating ordered droplet clusters: Stability, symmetry, and Voronoi Entropy","volume":"8","author":"Fedorets","year":"2017","journal-title":"J. Phys. Chem. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1103\/PhysRev.86.702","article-title":"On a theorem of irreversible thermodynamics","volume":"86","author":"Callen","year":"1952","journal-title":"Phys. Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1119\/1.13157","article-title":"Le Ch\u00e2telier reciprocal relations and the mechanical analog","volume":"51","author":"Gilmore","year":"1983","journal-title":"Am. J. Phys."},{"key":"ref_13","unstructured":"Tolman, R.C. (1934). Relativity, Themodynamics and Cosmology, Oxford University Press."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3762","DOI":"10.1103\/PhysRevLett.76.3762","article-title":"Evidence for convective effects in breath figure formation on volatile fluid surfaces","volume":"76","author":"Limaye","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"116103","DOI":"10.1103\/PhysRevLett.99.116103","article-title":"Controlling pattern formation in nanoparticle assemblies via directed solvent dewetting","volume":"99","author":"Martin","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","unstructured":"Frenkel, M., Legchenkova, I., and Bormashenko, E. (2019). Voronoi diagrams generated by the Archimedes spiral: Aesthetics vs. mathematics. Entropy, submitted."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/251\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:36:48Z","timestamp":1760186208000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/3\/251"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,6]]},"references-count":16,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["e21030251"],"URL":"https:\/\/doi.org\/10.3390\/e21030251","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,3,6]]}}}