{"id":"https://openalex.org/W2729901969","doi":"https://doi.org/10.3390/e19070322","title":"Entropic Phase Maps in Discrete Quantum Gravity","display_name":"Entropic Phase Maps in Discrete Quantum Gravity","publication_year":2017,"publication_date":"2017-06-30","ids":{"openalex":"https://openalex.org/W2729901969","doi":"https://doi.org/10.3390/e19070322","mag":"2729901969"},"language":"en","primary_location":{"id":"doi:10.3390/e19070322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070322","pdf_url":"https://www.mdpi.com/1099-4300/19/7/322/pdf?version=1500962901","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/7/322/pdf?version=1500962901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050269199","display_name":"Benjamin F. Dribus","orcid":"https://orcid.org/0009-0001-4802-3864"},"institutions":[{"id":"https://openalex.org/I161088229","display_name":"William Carey University","ror":"https://ror.org/03r7c7356","country_code":"US","type":"education","lineage":["https://openalex.org/I161088229"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Benjamin Dribus","raw_affiliation_strings":["Department of Mathematics, William Carey University, 710 William Carey Parkway, Hattiesburg, MS 39401, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, William Carey University, 710 William Carey Parkway, Hattiesburg, MS 39401, USA","institution_ids":["https://openalex.org/I161088229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050269199"],"corresponding_institution_ids":["https://openalex.org/I161088229"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3659,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.63446838,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"19","issue":"7","first_page":"322","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9969000220298767,"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/T11804","display_name":"Quantum many-body systems","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/phase-space","display_name":"Phase space","score":0.5683886408805847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5098575949668884},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4733854830265045},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"Quantum gravity","score":0.4459958076477051},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.42512667179107666},{"id":"https://openalex.org/keywords/causal-sets","display_name":"Causal sets","score":0.4157019555568695},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3235042691230774},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3101462721824646},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22740063071250916},{"id":"https://openalex.org/keywords/quantum-field-theory-in-curved-spacetime","display_name":"Quantum field theory in curved spacetime","score":0.09832799434661865}],"concepts":[{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5683886408805847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5098575949668884},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4733854830265045},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.4459958076477051},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42512667179107666},{"id":"https://openalex.org/C41254897","wikidata":"https://www.wikidata.org/wiki/Q1139715","display_name":"Causal sets","level":5,"score":0.4157019555568695},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3235042691230774},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3101462721824646},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22740063071250916},{"id":"https://openalex.org/C120484201","wikidata":"https://www.wikidata.org/wiki/Q2246697","display_name":"Quantum field theory in curved spacetime","level":4,"score":0.09832799434661865}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/e19070322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070322","pdf_url":"https://www.mdpi.com/1099-4300/19/7/322/pdf?version=1500962901","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":"pmh:oai:doaj.org/article:4a62d5823d554076b978df82d576db90","is_oa":true,"landing_page_url":"https://doaj.org/article/4a62d5823d554076b978df82d576db90","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 19, Iss 7, p 322 (2017)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e19070322","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19070322","pdf_url":"https://www.mdpi.com/1099-4300/19/7/322/pdf?version=1500962901","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":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W7398728","https://openalex.org/W999166514","https://openalex.org/W1472049032","https://openalex.org/W1506859129","https://openalex.org/W1879806639","https://openalex.org/W1947273351","https://openalex.org/W1973638500","https://openalex.org/W1975153182","https://openalex.org/W1980756322","https://openalex.org/W1984270176","https://openalex.org/W1987754386","https://openalex.org/W1997093580","https://openalex.org/W2003125936","https://openalex.org/W2004239847","https://openalex.org/W2004937076","https://openalex.org/W2016212637","https://openalex.org/W2018883342","https://openalex.org/W2026051065","https://openalex.org/W2027574092","https://openalex.org/W2045940223","https://openalex.org/W2053711071","https://openalex.org/W2055748416","https://openalex.org/W2062068040","https://openalex.org/W2075036653","https://openalex.org/W2076364902","https://openalex.org/W2077470755","https://openalex.org/W2078146385","https://openalex.org/W2079664466","https://openalex.org/W2081629270","https://openalex.org/W2093882311","https://openalex.org/W2132272743","https://openalex.org/W2154858141","https://openalex.org/W2157084252","https://openalex.org/W2166375060","https://openalex.org/W2317939109","https://openalex.org/W2407112624","https://openalex.org/W2486528160","https://openalex.org/W2609732865","https://openalex.org/W2950010724","https://openalex.org/W2963013185","https://openalex.org/W2963978562","https://openalex.org/W3037089749","https://openalex.org/W3099661704","https://openalex.org/W3100015866","https://openalex.org/W3100180512","https://openalex.org/W3101061617","https://openalex.org/W3101084584","https://openalex.org/W3101107119","https://openalex.org/W3102470562","https://openalex.org/W3103652464","https://openalex.org/W3104208124","https://openalex.org/W3105353076","https://openalex.org/W3123808419","https://openalex.org/W4233500204","https://openalex.org/W4246682128","https://openalex.org/W7071254480"],"related_works":["https://openalex.org/W1564982570","https://openalex.org/W3098241628","https://openalex.org/W2727014074","https://openalex.org/W3103420882","https://openalex.org/W3123673463","https://openalex.org/W4291338810","https://openalex.org/W2764084647","https://openalex.org/W4321320419","https://openalex.org/W2950144511","https://openalex.org/W1643914899"],"abstract_inverted_index":{"Path":[0,52],"summation":[1,17,53],"offers":[2],"a":[3,21,27,88,98,138,181],"flexible":[4],"general":[5],"approach":[6],"to":[7,97],"quantum":[8,11,67,134],"theory,":[9],"including":[10],"gravity.":[12],"In":[13],"the":[14,46,92,103,125,204],"latter":[15],"setting,":[16],"is":[18,183],"performed":[19],"over":[20,41],"space":[22,93],"of":[23,57,62,74,94,127,140,148,151,164,169,179,200,207],"evolutionary":[24,80,95],"pathways":[25,96],"in":[26,45,55,146,177],"history":[28],"configuration":[29],"space.":[30],"Discrete":[31],"causal":[32,50],"histories":[33,59],"called":[34,84,153,184],"acyclic":[35],"directed":[36],"sets":[37],"offer":[38],"certain":[39],"advantages":[40],"similar":[42],"models":[43],"appearing":[44],"literature,":[47],"such":[48,101,114,157,180],"as":[49,102,115,158,196],"sets.":[51],"defined":[54,145,176],"terms":[56,147,178],"these":[58],"enables":[60],"derivation":[61],"discrete":[63,133],"Schr\u00f6dinger-type":[64],"equations":[65],"describing":[66],"spacetime":[68],"dynamics":[69],"for":[70,132],"any":[71],"suitable":[72,129],"choice":[73],"algebraic":[75],"quantities":[76],"associated":[77,190],"with":[78],"each":[79],"pathway.":[81],"These":[82],"quantities,":[83],"phases,":[85],"collectively":[86],"define":[87],"phase":[89,130,174,187],"map":[90,175],"from":[91],"target":[99],"object,":[100],"unit":[104],"circle":[105],"S":[106,116,119,141],"1":[107,142],"\u2282":[108],"C":[109],",":[110],"or":[111,118],"an":[112,185,197],"analogue":[113],"3":[117],"7":[120],".":[121],"This":[122],"paper":[123],"explores":[124],"problem":[126],"identifying":[128],"maps":[131,144],"gravity,":[135],"focusing":[136],"on":[137],"class":[139],"-valued":[143],"\u201cstructural":[149],"increments\u201d":[150],"histories,":[152],"terminal":[154],"states.":[155],"Invariants":[156],"state":[159],"automorphism":[160],"groups":[161],"determine":[162],"multiplicities":[163],"states,":[165],"and":[166,203],"induce":[167],"families":[168],"natural":[170],"entropy":[171],"functions.":[172],"A":[173],"function":[182],"entropic":[186],"map.":[188],"The":[189],"dynamical":[191],"law":[192,206],"may":[193],"be":[194],"viewed":[195],"abstract":[198],"combination":[199],"Schr\u00f6dinger\u2019s":[201],"equation":[202],"second":[205],"thermodynamics.":[208]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}