{"id":"https://openalex.org/W2008874720","doi":"https://doi.org/10.1017/s0960129512000126","title":"Equilibrium and termination II: the case of Petri nets","display_name":"Equilibrium and termination II: the case of Petri nets","publication_year":2013,"publication_date":"2013-02-28","ids":{"openalex":"https://openalex.org/W2008874720","doi":"https://doi.org/10.1017/s0960129512000126","mag":"2008874720"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129512000126","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129512000126","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111482850","display_name":"Vincent Danos","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"VINCENT DANOS","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email:","School of Informatics, Laboratory for Foundations of Computer Science"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email:","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Informatics, Laboratory for Foundations of Computer Science","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032667158","display_name":"Nicolas Oury","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"NICOLAS OURY","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email:"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, United Kingdom Email:","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111482850"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":2.5378,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89103284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"290","last_page":"307"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9944999814033508,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.9944999814033508,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11195","display_name":"Simulation Techniques and Applications","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/petri-net","display_name":"Petri net","score":0.7303879261016846},{"id":"https://openalex.org/keywords/detailed-balance","display_name":"Detailed balance","score":0.5568375587463379},{"id":"https://openalex.org/keywords/stochastic-petri-net","display_name":"Stochastic Petri net","score":0.5465736389160156},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5458399057388306},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5233653783798218},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4934176504611969},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42355722188949585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41667842864990234},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.41222649812698364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3674396276473999},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.314717173576355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12261593341827393},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.089989572763443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06741046905517578}],"concepts":[{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.7303879261016846},{"id":"https://openalex.org/C135694725","wikidata":"https://www.wikidata.org/wiki/Q1201087","display_name":"Detailed balance","level":2,"score":0.5568375587463379},{"id":"https://openalex.org/C197551870","wikidata":"https://www.wikidata.org/wiki/Q7617809","display_name":"Stochastic Petri net","level":3,"score":0.5465736389160156},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5458399057388306},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5233653783798218},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4934176504611969},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42355722188949585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41667842864990234},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.41222649812698364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3674396276473999},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.314717173576355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12261593341827393},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.089989572763443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06741046905517578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129512000126","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129512000126","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8999999761581421,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G2160003213","display_name":null,"funder_award_id":"BB/D019621/1","funder_id":"https://openalex.org/F4320334629","funder_display_name":"Biotechnology and Biological Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334629","display_name":"Biotechnology and Biological Sciences Research Council","ror":"https://ror.org/00cwqg982"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W19838944","https://openalex.org/W77439205","https://openalex.org/W1500381309","https://openalex.org/W1586735752","https://openalex.org/W1787979754","https://openalex.org/W1892851289","https://openalex.org/W1965694523","https://openalex.org/W1969553191","https://openalex.org/W1975845571","https://openalex.org/W1986649132","https://openalex.org/W1996527169","https://openalex.org/W1997088148","https://openalex.org/W2001296126","https://openalex.org/W2007006124","https://openalex.org/W2011835017","https://openalex.org/W2027857026","https://openalex.org/W2040860090","https://openalex.org/W2047695579","https://openalex.org/W2054776476","https://openalex.org/W2063366436","https://openalex.org/W2075260598","https://openalex.org/W2075786206","https://openalex.org/W2094781369","https://openalex.org/W2104855667","https://openalex.org/W2106001218","https://openalex.org/W2115354930","https://openalex.org/W2122356930","https://openalex.org/W2126852846","https://openalex.org/W2131753537","https://openalex.org/W2135320702","https://openalex.org/W2144063122","https://openalex.org/W2146099270","https://openalex.org/W2147568833","https://openalex.org/W2148570690","https://openalex.org/W2175715045","https://openalex.org/W2611943439","https://openalex.org/W3105045141","https://openalex.org/W3142588439","https://openalex.org/W4244873611","https://openalex.org/W6652212618"],"related_works":["https://openalex.org/W1543378523","https://openalex.org/W2126080849","https://openalex.org/W1491709828","https://openalex.org/W2916743419","https://openalex.org/W2381491984","https://openalex.org/W2257573499","https://openalex.org/W2148229336","https://openalex.org/W1980200158","https://openalex.org/W1513546254","https://openalex.org/W2091203523"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,34],"concerned":[3],"with":[4,16],"the":[5,27,42,48,88,95],"asymptotic":[6],"properties":[7],"of":[8,12,29,50,99],"a":[9,22,59,67],"restricted":[10],"class":[11],"Petri":[13,100],"nets":[14],"equipped":[15],"stochastic":[17],"mass-action":[18],"semantics.":[19],"We":[20,53],"establish":[21],"simple":[23],"algebraic":[24],"criterion":[25],"for":[26],"existence":[28],"an":[30,37,73,78],"equilibrium":[31],",":[32],"that":[33,40,56,71],"to":[35],"say,":[36],"invariant":[38],"probability":[39,60],"satisfies":[41],"detailed":[43],"balance":[44],"condition":[45],"familiar":[46],"from":[47],"thermodynamics":[49],"reaction":[51],"networks.":[52],"also":[54],"find":[55],"when":[57],"such":[58],"exists,":[61],"it":[62],"can":[63,91],"be":[64,92],"described":[65],"by":[66],"free":[68],"energy":[69,75],"function":[70],"combines":[72],"internal":[74],"term":[76,90],"and":[77],"entropy":[79,89],"term.":[80],"Under":[81],"strong":[82],"additional":[83],"conditions,":[84],"we":[85],"show":[86],"how":[87],"deconstructed":[93],"using":[94],"finer-grained":[96],"individual-token":[97],"semantics":[98],"nets.":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
