{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T15:58:21Z","timestamp":1791475101324,"version":"4.3.4"},"reference-count":106,"publisher":"American Chemical Society (ACS)","issue":"40","license":[{"start":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T00:00:00Z","timestamp":1790380800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T00:00:00Z","timestamp":1790380800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T00:00:00Z","timestamp":1790380800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/100000008","name":"David and Lucile Packard Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000008","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0024154"],"award-info":[{"award-number":["DE-SC0024154"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22433006"],"award-info":[{"award-number":["22433006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Collective light\u2013matter systems host an extensive manifold of dark states whose role in the emergence of thermodynamic behavior remains poorly understood, especially in the presence of disorder and structured environments. Here, we develop a hybrid matrix product state\u2013hierarchical equations of motion (MPS\u2013HEOM) approach that enables numerically exact simulations of polariton dynamics from a few emitters to the thermodynamic limit under both static and dynamic disorder. This allows us, for the first time, to provide a quantitative and operational answer to the long-standing question of what is the minimum system size required for single-excitation photonic dynamics to reach the thermodynamic limit in collective polaritonic systems. By introducing a convergence scale, NT, i.e., the number of molecules required for the photonic dynamics to reach the thermodynamic limit, we show that dynamic disorder generally poses a greater computational challenge than static disorder. We attribute this behavior to the suppression of collective light\u2013matter dynamics by disorder, which dynamically activates non-collective degrees of freedom. We further find that NT exhibits a turnover behavior as the bath becomes more Markovian, as the bath time scales regulate bright-to-dark energy transfer and the involvement of dark and gray states. Hence, phonon time scales control both the breakdown of collective behavior and the growth of NT. Our results establish the suppression of collective behavior as the key mechanism governing thermodynamic convergence in disordered light\u2013matter systems.<\/jats:p>","DOI":"10.1021\/acs.jpclett.6c02068","type":"journal-article","created":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T06:01:30Z","timestamp":1790402490000},"page":"11453-11460","source":"Crossref","is-referenced-by-count":1,"title":["For Molecular\nPolaritons, Disorder and Phonon Time\nScales Control the Activation of Dark States in the Thermodynamic\nLimit"],"prefix":"10.1021","volume":"17","author":[{"given":"Tianchu","family":"Li","sequence":"first","affiliation":[{"name":"University of Colorado Boulder , , , ,","place":["Boulder, Colorado, United States, 80309"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pranay","family":"Venkatesh","sequence":"additional","affiliation":[{"name":"University of Colorado Boulder , , , ,","place":["Boulder, Colorado, United States, 80309"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9046-2924","authenticated-orcid":true,"given":"Qiang","family":"Shi","sequence":"additional","affiliation":[{"name":"Institute of Chemistry, Chinese Academy of Sciences , , ,","place":["Beijing, Zhongguancun, China, 100190"]},{"name":"University of Chinese Academy of Sciences , ,","place":["Beijing, China, 100049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3037-3695","authenticated-orcid":true,"given":"Andre\u0301s","family":"Montoya-Castillo","sequence":"additional","affiliation":[{"name":"University of Colorado Boulder , , , ,","place":["Boulder, Colorado, United States, 80309"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,26]]},"reference":[{"key":"2026100811155430000_cit1","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1103\/PhysRev.112.1555","article-title":"Theory\nof the Contribution of Excitons to the Complex Dielectric Constant\nof Crystals","volume":"112","author":"Hopfield","year":"1958","journal-title":"Phys. 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Lett."},{"key":"2026100811155430000_cit35","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1039\/C8CS00193F","article-title":"Strong light\u2013matter\ninteractions: a new direction within chemistry","volume":"48","author":"Hertzog","year":"2019","journal-title":"Chem. Soc. Rev."},{"key":"2026100811155430000_cit36","volume-title":"Organic Molecular Crystals:\nInteraction, Localization, and Transport Phenomena","author":"Silinsh","year":"1994"},{"key":"2026100811155430000_cit37","doi-asserted-by":"publisher","first-page":"173001","DOI":"10.1103\/PhysRevLett.129.173001","article-title":"Efficient many-body non-Markovian\ndynamics of organic polaritons","volume":"129","author":"Fowler-Wright","year":"2022","journal-title":"Phys. Rev. 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Res."},{"key":"2026100811155430000_cit54","doi-asserted-by":"publisher","first-page":"134106","DOI":"10.1063\/5.0227515","article-title":"One molecule to couple them all:\nToward realistic numbers of molecules in multiscale molecular dynamics\nsimulations of exciton-polaritons","volume":"161","author":"Sokolovskii","year":"2024","journal-title":"J. Chem.\nPhys."},{"key":"2026100811155430000_cit55","doi-asserted-by":"publisher","first-page":"227401","DOI":"10.1103\/PhysRevLett.121.227401","article-title":"Tensor network simulation of non-Markovian dynamics\nin organic polaritons","volume":"121","author":"Del Pino","year":"2018","journal-title":"Phys. Rev. Lett."},{"key":"2026100811155430000_cit56","doi-asserted-by":"publisher","first-page":"223601","DOI":"10.1103\/PhysRevLett.118.223601","article-title":"Dark vibronic polaritons\nand the spectroscopy of organic\nmicrocavities","volume":"118","author":"Herrera","year":"2017","journal-title":"Phys. Rev. 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