{"id":"https://openalex.org/W4408054111","doi":"https://doi.org/10.3390/e27030258","title":"The Glass Transition: A Topological Perspective","display_name":"The Glass Transition: A Topological Perspective","publication_year":2025,"publication_date":"2025-02-28","ids":{"openalex":"https://openalex.org/W4408054111","doi":"https://doi.org/10.3390/e27030258","pmid":"https://pubmed.ncbi.nlm.nih.gov/40149182"},"language":"en","primary_location":{"id":"doi:10.3390/e27030258","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27030258","pdf_url":"https://www.mdpi.com/1099-4300/27/3/258/pdf?version=1740754697","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/3/258/pdf?version=1740754697","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075362850","display_name":"Arthur Vesperini","orcid":"https://orcid.org/0000-0003-1823-4406"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I4210163778","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Perugia","ror":"https://ror.org/05478fx36","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210163778"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Arthur Vesperini","raw_affiliation_strings":["Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy","INFN Sezione di Perugia, 06123 Perugia, Italy"],"raw_orcid":"https://orcid.org/0000-0003-1823-4406","affiliations":[{"raw_affiliation_string":"Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"INFN Sezione di Perugia, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I4210163778"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074457878","display_name":"Roberto Franzosi","orcid":"https://orcid.org/0000-0001-7588-921X"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]},{"id":"https://openalex.org/I4210163778","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Perugia","ror":"https://ror.org/05478fx36","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210163778"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Roberto Franzosi","raw_affiliation_strings":["Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy","INFN Sezione di Perugia, 06123 Perugia, Italy"],"raw_orcid":"https://orcid.org/0000-0001-7588-921X","affiliations":[{"raw_affiliation_string":"Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"INFN Sezione di Perugia, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I4210163778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044783610","display_name":"Marco Pettini","orcid":"https://orcid.org/0000-0003-1561-4390"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I137853757","display_name":"Howard University","ror":"https://ror.org/05gt1vc06","country_code":"US","type":"education","lineage":["https://openalex.org/I137853757"]},{"id":"https://openalex.org/I143002897","display_name":"Universit\u00e9 de Toulon","ror":"https://ror.org/02m9kbe37","country_code":"FR","type":"education","lineage":["https://openalex.org/I143002897"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210160215","display_name":"Centre de Physique Th\u00e9orique","ror":"https://ror.org/052bbtn31","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210098836","https://openalex.org/I4210160215"]}],"countries":["FR","US"],"is_corresponding":true,"raw_author_name":"Marco Pettini","raw_affiliation_strings":["Aix-Marseille University, Universit\u00e9 de Toulon, CNRS, 13288 Marseille, France","Centre de Physique Th\u00e9orique, 13288 Marseille, France","Quantum Biology Lab, Howard University, Washington, DC 20059, USA"],"raw_orcid":"https://orcid.org/0000-0003-1561-4390","affiliations":[{"raw_affiliation_string":"Aix-Marseille University, Universit\u00e9 de Toulon, CNRS, 13288 Marseille, France","institution_ids":["https://openalex.org/I143002897","https://openalex.org/I1294671590","https://openalex.org/I21491767"]},{"raw_affiliation_string":"Centre de Physique Th\u00e9orique, 13288 Marseille, France","institution_ids":["https://openalex.org/I4210160215"]},{"raw_affiliation_string":"Quantum Biology Lab, Howard University, Washington, DC 20059, USA","institution_ids":["https://openalex.org/I137853757"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044783610"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I137853757","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210160215"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.2701,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79199877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"27","issue":"3","first_page":"258","last_page":"258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10799","display_name":"Data Visualization and Analytics","score":0.9555000066757202,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.554772675037384},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5362713932991028},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5073007941246033},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4989044666290283},{"id":"https://openalex.org/keywords/frustration","display_name":"Frustration","score":0.498584508895874},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.45580294728279114},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4164550006389618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3121912181377411},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13453641533851624},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11371389031410217},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.08926478028297424},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08840548992156982}],"concepts":[{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.554772675037384},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5362713932991028},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5073007941246033},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4989044666290283},{"id":"https://openalex.org/C38710091","wikidata":"https://www.wikidata.org/wiki/Q192242","display_name":"Frustration","level":2,"score":0.498584508895874},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.45580294728279114},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4164550006389618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3121912181377411},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13453641533851624},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11371389031410217},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.08926478028297424},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08840548992156982}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e27030258","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27030258","pdf_url":"https://www.mdpi.com/1099-4300/27/3/258/pdf?version=1740754697","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40149182","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40149182","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:usiena-air.unisi.it:11365/1292415","is_oa":true,"landing_page_url":"https://www.mdpi.com/1099-4300/27/3/258","pdf_url":"https://www.mdpi.com/1099-4300/27/3/258/pdf","source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-05492861v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05492861","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, 2025, 27 (3), pp.258. ⟨10.3390/e27030258⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:4f38c6d513be4713bae89a5daf8c9588","is_oa":false,"landing_page_url":"https://doaj.org/article/4f38c6d513be4713bae89a5daf8c9588","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 3, p 258 (2025)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:11941106","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11941106","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e27030258","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27030258","pdf_url":"https://www.mdpi.com/1099-4300/27/3/258/pdf?version=1740754697","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408054111.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2380568010","https://openalex.org/W2370937237","https://openalex.org/W921996089","https://openalex.org/W2364246437","https://openalex.org/W2386183613","https://openalex.org/W2348739292","https://openalex.org/W2100120627","https://openalex.org/W2374204729","https://openalex.org/W2057412136","https://openalex.org/W2492927755"],"abstract_inverted_index":{"Resorting":[0],"to":[1,35,52,98],"microcanonical":[2],"ensemble":[3],"Monte":[4],"Carlo":[5],"simulations,":[6],"we":[7],"study":[8],"the":[9,15,69,74,77,80,84,87,99,103,114,123,126,142],"geometric":[10],"and":[11,47,83,91],"topological":[12,100,143],"properties":[13,101],"of":[14,18,21,68,79,86,102,125,145],"state":[16],"space":[17],"a":[19,22,27],"model":[20],"network":[23],"glass-former.":[24],"This":[25,130],"model,":[26],"Lennard-Jones":[28],"binary":[29],"mixture,":[30],"does":[31],"not":[32],"crystallize":[33],"due":[34],"frustration.":[36],"We":[37],"have":[38],"found":[39],"two":[40],"peaks":[41],"in":[42,55,65,122],"specific":[43],"heat":[44],"at":[45,48],"equilibrium":[46],"low":[49],"energy,":[50],"corresponding":[51],"important":[53,131],"changes":[54,121],"local":[56],"ordering.":[57],"These":[58],"singularities":[59],"were":[60],"accompanied":[61],"by":[62],"inflection":[63],"points":[64],"geometrical":[66],"markers":[67],"potential":[70],"energy":[71,127],"level":[72,128],"sets-namely,":[73],"mean":[75],"curvature,":[76],"dispersion":[78],"principal":[81],"curvatures,":[82],"variance":[85],"scalar":[88],"curvature.":[89],"Pinkall's":[90],"Overholt's":[92],"theorems":[93],"closely":[94],"relate":[95],"these":[96],"quantities":[97],"accessible":[104],"state-space":[105],"manifold.":[106],"Thus,":[107],"our":[108],"analysis":[109],"provides":[110],"strong":[111],"indications":[112],"that":[113,134],"glass":[115],"transition":[116,137],"is":[117],"associated":[118],"with":[119],"major":[120],"topology":[124],"sets.":[129],"result":[132],"suggests":[133],"this":[135],"phase":[136,146],"can":[138],"be":[139],"understood":[140],"through":[141],"theory":[144],"transitions.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}