{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T11:40:38Z","timestamp":1759405238429,"version":"build-2065373602"},"reference-count":35,"publisher":"AIP Publishing","issue":"13","funder":[{"DOI":"10.13039\/501100024870","name":"Exacte en Natuurwetenschappen","doi-asserted-by":"publisher","award":["VI.VIDI.192.102"],"award-info":[{"award-number":["VI.VIDI.192.102"]}],"id":[{"id":"10.13039\/501100024870","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,10,7]]},"abstract":"<jats:p>Understanding the role that structure plays in the dynamical arrest observed in glassy systems remains an open challenge. Over the past decade, machine learning (ML) strategies have emerged as an important tool for probing this structure\u2013dynamics relationship, particularly for predicting heterogeneous glassy dynamics from local structure. A recent advancement is the introduction of the cage state, a structural quantity that captures the average positions of particles while rearrangements are forbidden. During the caging regime, linear models trained on the cage state have been shown to outperform more complex ML methods trained on initial configurations only. In this paper, we explore the properties associated with the cage state in more detail to better understand why it serves as such an effective predictor for the dynamics. In particular, we examine how the cage state in a binary hard-sphere mixture is influenced by both packing fraction and boundary conditions. Our results reveal that, as the system approaches the glassy regime, the cage state becomes increasingly influenced by long-range structural effects. This influence is evident both in its predictive power for particle dynamics and in the internal structure of the cage state, suggesting that the CS might be associated with some form of an amorphous growing structural length scale.<\/jats:p>","DOI":"10.1063\/5.0292330","type":"journal-article","created":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T11:02:30Z","timestamp":1759402950000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Characterizing the cage state of glassy systems and its sensitivity to frozen boundaries"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3689-6027","authenticated-orcid":false,"given":"Rinske M.","family":"Alkemade","sequence":"first","affiliation":[{"name":"Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University 1 , Utrecht,","place":["Netherlands"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9401-6067","authenticated-orcid":false,"given":"Frank","family":"Smallenburg","sequence":"additional","affiliation":[{"name":"Laboratoire de Physique des Solides, Universit\u00e9 Paris-Saclay, CNRS 2 , 91405 Orsay,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9432-9680","authenticated-orcid":false,"given":"Laura","family":"Filion","sequence":"additional","affiliation":[{"name":"Soft Condensed Matter, Debye Institute of Nanomaterials Science, Utrecht University 1 , Utrecht,","place":["Netherlands"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,10,2]]},"reference":[{"key":"2025100207022199400_c1","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.physrep.2009.03.003","article-title":"Supercooled liquids for pedestrians","volume":"476","year":"2009","journal-title":"Phys. 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