{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T09:02:05Z","timestamp":1789635725082,"version":"4.0.0"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T00:00:00Z","timestamp":1789084800000},"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>Recent lattice studies have revealed that the color flux tube between static quark\u2013antiquark pairs exhibits an excess entanglement entropy (flux-tube entanglement entropy, FTE2) that scales linearly with the quark separation L. In this paper, we demonstrate similar behavior in a string-net model based on SU(2)k fusion categories, where the nontrivial object j=1\/2 (analogous to color charge) cannot exist in isolation due to the fusion rules, naturally exhibiting \u201cconfinement\u201d. We compute the entanglement entropy of the flux tube connecting two j=1\/2 objects using the microcanonical (equal-weight) prescription S(R)=ln(dim(Hom(R))) and find an entropy density \u03c3k=lnd1\/2=ln(2cos\u03c0k+2). For k=3, the category reduces to the Fibonacci case, yielding an entropy density \u03c33 = ln \u03c6 \u2248 0.4812 (\u03c6 is the golden ratio), which is qualitatively comparable in magnitude to the scale inferred from lattice studies and the entropy surface mechanism. Under a thermalization assumption for the fusion-channel degrees of freedom, minimizing the free energy F=(J\u2212T\u03c3k)L yields a confinement\u2013deconfinement transition at (Tc=J\/\u03c3k), which is first-order-like (tension sign reversal) rather than a continuous critical transition. The parameter k offers a tunable knob, making the SU(2)k family a computable laboratory for entropic confinement. The predicted entropy-density jump can be directly tested in quantum simulator platforms (e.g., Rydberg arrays or superconducting circuits) that realize Fibonacci anyonic models.<\/jats:p>","DOI":"10.3390\/e28091017","type":"journal-article","created":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T17:14:59Z","timestamp":1789146899000},"page":"1017","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropic Confinement in String-Net Models: An Analogue Study via SU(2)k Fusion Categories"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1690-057X","authenticated-orcid":false,"given":"Xiaodong","family":"Yang","sequence":"first","affiliation":[{"name":"CGNPC Uranium Resources Co., Ltd., Beijing 100072, China"},{"name":"School of Physics Science and Technology, Lanzhou University, Lanzhou 730000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0146-6410(03)90012-3","article-title":"The confinement problem in lattice gauge theory","volume":"51","author":"Greensite","year":"2003","journal-title":"Prog. 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