{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T04:45:49Z","timestamp":1785818749851,"version":"3.56.0"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004070","name":"Khalifa University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004070","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/05hffr360","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004070","name":"Khalifa University Research and Innovation","doi-asserted-by":"publisher","award":["KU-INT-RIG-2024-046\/8474000759"],"award-info":[{"award-number":["KU-INT-RIG-2024-046\/8474000759"]}],"id":[{"id":"10.13039\/501100004070","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Thousand Talents Program and the President\u2019s International Fellowship Initiative of the Chinese Academy of Sciences Awards"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Modern societies comprise overlapping communities whose opinions evolve on strongly interacting networks that are often mutually antagonistic. We introduce a minimal antagonistic multiplex consensus model in which each layer follows intra-layer majority-rule dynamics, while inter-layer interactions are inhibitory. A mean-field analysis shows that antagonistic coupling destabilizes the balanced state through an antisymmetric mode and favors two polarized absorbing states with opposite magnetization in the two layers. Network-averaged simulations confirm that small fluctuations near equal initial support determine which polarized state is ultimately reached: trajectories exhibit metastable delay, long convergence times, and a localized peak in the Shannon entropy of outcomes. A finite-size analysis with independent network realizations and bootstrap uncertainty estimates shows that the high-entropy interval narrows as \u0394r\u00a0\u223cN\u2212\u03b3eff, with \u03b3eff=0.513 and a 95% bootstrap confidence interval [0.489,0.526], consistent with finite-size sharpening controlled by fluctuations in the initial imbalance. We also perform network topology checks and find that the qualitatively antagonistic mechanism persists beyond random-regular graphs. As an illustrative empirical application, we analyze county-level results from the 2024 U.S. presidential election. The vote-share and entropy landscapes separate low-entropy partisan strongholds from higher-entropy competitive counties. Our results suggest that antagonistic multiplex coupling provides a simple mechanism by which polarized attractors and localized outcome uncertainty can arise together.<\/jats:p>","DOI":"10.3390\/e28080857","type":"journal-article","created":{"date-parts":[[2026,8,3]],"date-time":"2026-08-03T15:51:23Z","timestamp":1785772283000},"page":"857","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Metastability and Entropy Peaks in Antagonistic Multiplex Consensus Dynamics"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3682-7408","authenticated-orcid":false,"given":"Jack C. M.","family":"Hughes","sequence":"first","affiliation":[{"name":"Department of Public Health and Epidemiology, College of Medicine and Health Sciences, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"},{"name":"Department of Physics, College of Engineering and Physical Sciences, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3206-424X","authenticated-orcid":false,"given":"Anna","family":"Kusmartseva","sequence":"additional","affiliation":[{"name":"Department of Physics, Loughborough University, Loughborough LE11 3TU, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3748-4961","authenticated-orcid":false,"given":"Glenn","family":"Muschert","sequence":"additional","affiliation":[{"name":"Department of Public Health and Epidemiology, College of Medicine and Health Sciences, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"},{"name":"Healthcare Engineering Innovation Group (HEIG), Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5457-6193","authenticated-orcid":false,"given":"Herbert F.","family":"Jelinek","sequence":"additional","affiliation":[{"name":"Healthcare Engineering Innovation Group (HEIG), Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"},{"name":"Department of Medical Sciences, College of Medicine and Health Sciences, Khalifa University, Abu Dhabi P.O. Box 127788, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5643-0526","authenticated-orcid":false,"given":"Fedor V.","family":"Kusmartsev","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Engineering and Physical Sciences, Khalifa University, Abu Dhabi P.O. 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