{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:42:48Z","timestamp":1759970568140,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["25400465"],"award-info":[{"award-number":["25400465"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Spontaneous pattern formation is a universal phenomenon that occurs in purely physical systems, biology, and human societies. Salt fingering due to differential diffusion of heat and salt in seawater is a typical example, although the general principle that governs pattern formation remains unknown. We show through simple experiments injecting a salt solution into a sucrose solution of equal density that a salt finger exhibits characteristic pattern transitions depending on the injection flow rate. When the rate increases, a linear finger starts meandering, branching, and multiple branching, whereas when the rate is decreased, it produces a beading pattern. These morphological instabilities and associated pattern formation are caused by a local accumulation of kinetic energy that minimizes the flow resistance and maximizes the energy dissipation in the final steady state. We suggest that this energy accumulation mechanism governs a wide variety of pattern formation phenomena in non-equilibrium systems, including morphogenesis of abiotic protocells.<\/jats:p>","DOI":"10.3390\/e27020106","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T11:09:02Z","timestamp":1737544142000},"page":"106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Thermodynamics of Morphogenesis: Beading and Branching Pattern Formation in Diffusion-Driven Salt Finger Plumes"],"prefix":"10.3390","volume":"27","author":[{"given":"Hisashi","family":"Ozawa","sequence":"first","affiliation":[{"name":"Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima 739-8521, Japan"},{"name":"School of Integrated Arts and Sciences, Hiroshima University, Hiroshima 739-8521, Japan"}]},{"given":"Sayaka","family":"Murayama-Ogino","sequence":"additional","affiliation":[{"name":"School of Integrated Arts and Sciences, Hiroshima University, Hiroshima 739-8521, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3798-0730","authenticated-orcid":false,"given":"Axel","family":"Kleidon","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Biogeochemistry, 07701 Jena, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"ref_1","unstructured":"Thompson, D.W. 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