{"id":"https://openalex.org/W2139757104","doi":"https://doi.org/10.1140/epjc/s10052-015-3641-0","title":"A note on Maxwell\u2019s equal area law for black hole phase transition","display_name":"A note on Maxwell\u2019s equal area law for black hole phase transition","publication_year":2015,"publication_date":"2015-09-01","ids":{"openalex":"https://openalex.org/W2139757104","doi":"https://doi.org/10.1140/epjc/s10052-015-3641-0","mag":"2139757104"},"language":"en","primary_location":{"id":"doi:10.1140/epjc/s10052-015-3641-0","doi":"https://doi.org/10.1140/epjc/s10052-015-3641-0","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3641-0","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3641-0.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3641-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085557029","display_name":"Shan-Quan Lan","orcid":"https://orcid.org/0000-0002-1140-900X","observed_orcids":["https://orcid.org/0000-0002-1140-900X"]},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan-Quan Lan","raw_affiliation_strings":["Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","BEIJING NORMAL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"BEIJING NORMAL UNIVERSITY","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025458892","display_name":"Jie-Xiong Mo","orcid":"https://orcid.org/0000-0002-8527-4005","observed_orcids":["https://orcid.org/0000-0002-8527-4005"]},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie-Xiong Mo","raw_affiliation_strings":["Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","BEIJING NORMAL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"BEIJING NORMAL UNIVERSITY","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038218546","display_name":"Wenbiao Liu","orcid":"https://orcid.org/0000-0001-5271-2307","observed_orcids":["https://orcid.org/0000-0001-5271-2307"]},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wen-Biao Liu","raw_affiliation_strings":["Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","BEIJING NORMAL UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Institute of Theoretical Physics, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"BEIJING NORMAL UNIVERSITY","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038218546"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":2.6738,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.89463456,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"75","issue":"9","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10744","display_name":"Astrophysical Phenomena and Observations","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/black-hole-phase-transitions","display_name":"black hole phase transitions","score":0.949999988079071},{"id":"https://openalex.org/keywords/charged-ads-black-holes","display_name":"charged AdS black holes","score":0.9860000014305115},{"id":"https://openalex.org/keywords/p-v-criticality","display_name":"P-V criticality","score":0.550000011920929},{"id":"https://openalex.org/keywords/black-hole-thermodynamics","display_name":"black hole thermodynamics","score":0.6259999871253967}],"concepts":[{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.6100578904151917},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6078563928604126},{"id":"https://openalex.org/C50341732","wikidata":"https://www.wikidata.org/wiki/Q880302","display_name":"Black hole (networking)","level":5,"score":0.5655225515365601},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5127407312393188},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4542456567287445},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4442586600780487},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4362666606903076},{"id":"https://openalex.org/C168907044","wikidata":"https://www.wikidata.org/wiki/Q7834431","display_name":"Transition point","level":2,"score":0.42680656909942627},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3327022194862366},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3299601376056671},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3047173321247101},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29276707768440247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28453329205513},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25770288705825806},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1430569589138031},{"id":"https://openalex.org/C104954878","wikidata":"https://www.wikidata.org/wiki/Q1648707","display_name":"Routing protocol","level":3,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.0},{"id":"https://openalex.org/C89305328","wikidata":"https://www.wikidata.org/wiki/Q1755411","display_name":"Link-state routing protocol","level":4,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1140/epjc/s10052-015-3641-0","doi":"https://doi.org/10.1140/epjc/s10052-015-3641-0","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3641-0","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3641-0.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1503.07658","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.07658","pdf_url":"https://arxiv.org/pdf/1503.07658","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:edpsciences.org:dkey/10.1140/epjc/s10052-015-3641-0","doi":null,"is_oa":false,"landing_page_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjc/s10052-015-3641-0","pdf_url":"http://www.springerlink.com/content/fulltext.pdf?id=doi:10.1140/epjc/s10052-015-3641-0","source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1140/epjc/s10052-015-3641-0","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1503.07658","doi":"https://doi.org/10.48550/arxiv.1503.07658","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.07658","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1140/epjc/s10052-015-3641-0","doi":"https://doi.org/10.1140/epjc/s10052-015-3641-0","is_oa":true,"landing_page_url":"https://doi.org/10.1140/epjc/s10052-015-3641-0","pdf_url":"https://link.springer.com/content/pdf/10.1140/epjc/s10052-015-3641-0.pdf","source":{"id":"https://openalex.org/S94052278","display_name":"The European Physical Journal C","issn_l":"1434-6044","issn":["1434-6044","1434-6052"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-a","jufo-2","ki-jl-1","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The European Physical Journal C","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1979257090","display_name":null,"funder_award_id":"11178007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2768482007","display_name":null,"funder_award_id":"11235003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G661663340","display_name":null,"funder_award_id":"11175019","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2139757104.pdf","grobid_xml":"https://content.openalex.org/works/W2139757104.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1512108348","https://openalex.org/W1823089390","https://openalex.org/W1889142700","https://openalex.org/W1908296820","https://openalex.org/W1922740389","https://openalex.org/W1972819072","https://openalex.org/W1981638536","https://openalex.org/W1981889200","https://openalex.org/W1996184991","https://openalex.org/W2003601124","https://openalex.org/W2013171989","https://openalex.org/W2017321902","https://openalex.org/W2034569348","https://openalex.org/W2039609754","https://openalex.org/W2056533655","https://openalex.org/W2060358789","https://openalex.org/W2063817222","https://openalex.org/W2067864025","https://openalex.org/W2072356206","https://openalex.org/W2076646969","https://openalex.org/W2087333092","https://openalex.org/W2087963558","https://openalex.org/W2088299329","https://openalex.org/W2100546634","https://openalex.org/W2103534121","https://openalex.org/W2112301627","https://openalex.org/W2129925474","https://openalex.org/W2164965693","https://openalex.org/W2165752861","https://openalex.org/W3000019265","https://openalex.org/W3098384847","https://openalex.org/W3100297110","https://openalex.org/W3104704332","https://openalex.org/W4249956767","https://openalex.org/W6600595061","https://openalex.org/W6836079571","https://openalex.org/W6992984786"],"related_works":["https://openalex.org/W2893498679","https://openalex.org/W2953062777","https://openalex.org/W2551191907","https://openalex.org/W2534308303","https://openalex.org/W1815641581","https://openalex.org/W2070345769","https://openalex.org/W2280214130","https://openalex.org/W2952354335","https://openalex.org/W2528218790","https://openalex.org/W3100297110"],"abstract_inverted_index":{"The":[0,53],"state":[1],"equation":[2],"of":[3,61],"the":[4,12,20,21,24,35,42,47,73,79,89,96,102,122],"charged":[5,63,111],"AdS":[6,64],"black":[7,65,112],"hole":[8,66,113],"is":[9,39,119],"reviewed":[10],"in":[11,41],"T\u2013":[13],"$$r_{+}$$":[14],"plane.":[15,93],"With":[16],"a":[17,62,109,114],"view":[18],"on":[19],"phase":[22,48,55,123],"transition,":[23],"T\u2013S,":[25,97],"P\u2013V,":[26],"P\u2013":[27,90],"$$\\nu":[28,91],"$$":[29,92],"graphs":[30],"are":[31],"plotted":[32],"and":[33,105],"then":[34],"equal":[36,80],"area":[37,81],"law":[38,82],"used":[40,86],"three":[43,74],"cases":[44],"to":[45,95],"get":[46],"transition":[49,56],"point":[50,57],"(P,":[51],"T).":[52],"analytical":[54],"relations":[58],"for":[59,88,108,121],"P\u2013T":[60],"has":[67],"been":[68],"obtained":[69],"successfully.":[70],"By":[71],"comparing":[72],"results,":[75,99],"we":[76,100],"find":[77,106],"that":[78,107],"possibly":[83],"cannot":[84],"be":[85],"directly":[87],"According":[94],"P\u2013V":[98],"plot":[101],"P\u2013T\u2013Q":[103],"graph":[104],"highly":[110],"very":[115],"low":[116],"temperature":[117],"condition":[118],"required":[120],"transition.":[124]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2016-06-24T00:00:00"}