{"id":"https://openalex.org/W2302739894","doi":null,"title":"Reversibility and irreversibility","display_name":"Reversibility and irreversibility","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2302739894","mag":"2302739894"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.151.4698","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.151.4698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ma.hw.ac.uk/~oliver/irrev.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5054196943","display_name":"O. Penrose","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"O. Penrose","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5054196943"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2108,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45071247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9779999852180481,"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"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9779999852180481,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.007300000172108412,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reversibility","display_name":"reversibility","score":0.9340000152587891},{"id":"https://openalex.org/keywords/irreversibility","display_name":"irreversibility","score":0.9990000128746033},{"id":"https://openalex.org/keywords/entropy","display_name":"entropy","score":0.4860000014305115},{"id":"https://openalex.org/keywords/second-law-of-thermodynamics","display_name":"second law of thermodynamics","score":0.9290000200271606},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.8009999990463257},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.828000009059906},{"id":"https://openalex.org/keywords/heat-equation","display_name":"heat equation","score":0.9480000138282776},{"id":"https://openalex.org/keywords/microscopic-dynamics","display_name":"microscopic dynamics","score":0.4449999928474426},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"classical mechanics","score":0.6589999794960022},{"id":"https://openalex.org/keywords/schrodinger-equation","display_name":"Schr\u00f6dinger equation","score":0.9760000109672546},{"id":"https://openalex.org/keywords/macroscopic-description","display_name":"macroscopic description","score":0.3440000116825104},{"id":"https://openalex.org/keywords/collision-integral","display_name":"collision integral","score":0.32600000500679016}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6141185164451599},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5877323746681213},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5294049978256226},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5166242718696594},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.5071759223937988},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5031515955924988},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.4741458594799042},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.4214981198310852},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.41702523827552795},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.4162932336330414},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3973689675331116},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2774466276168823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.151.4698","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.151.4698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ma.hw.ac.uk/~oliver/irrev.pdf","raw_type":"text"},{"id":"mag:2302739894","doi":null,"is_oa":false,"landing_page_url":"http://www.macs.hw.ac.uk/~oliver/irrev.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1568056205","https://openalex.org/W2010538207","https://openalex.org/W3100436695"],"related_works":["https://openalex.org/W10430598","https://openalex.org/W2035847264","https://openalex.org/W1511407836","https://openalex.org/W1997444424","https://openalex.org/W171712151","https://openalex.org/W1571216414","https://openalex.org/W2371351129","https://openalex.org/W1541283151","https://openalex.org/W203812677","https://openalex.org/W1037423551"],"abstract_inverted_index":{"In":[0],"order":[1],"of":[2,8,17,33,92,101,114,119],"increasing":[3],"detail,":[4],"some":[5],"well-known":[6],"forms":[7],"mathematical":[9],"description":[10],"for":[11,144],"a":[12,34,112],"material":[13,18],"object":[14],"or":[15,141],"system":[16,37,113,147],"objects":[19],"are:":[20],"1.":[21],"The":[22],"thermodynamic":[23],"description,":[24],"which":[25],"includes":[26],"the":[27,30,56,90,95,138,145],"principle":[28],"that":[29],"entropy":[31],"S":[32],"thermally":[35],"isolated":[36],"never":[38],"decreases":[39],"with":[40],"time:":[41],"if":[42],"t1":[43],"<":[44],"t2":[45],"then":[46],"S(t1)":[47],"\u2264":[48],"S(t2)":[49],"(1)":[50],"2.":[51],"Macroscopic":[52],"descriptions,":[53],"such":[54,71],"as":[55,72,111],"heat":[57],"equation":[58,74,143],"\u2202e/\u2202t":[59],"=":[60,80,126],"K":[61],"\u2207":[62],"2":[63,123,125],"T":[64],"(2)":[65],"3.":[66],"Descriptions":[67],"by":[68],"kinetic":[69],"equations":[70,118],"Boltzmann\u2019s":[73],"\u2202f/\u2202t":[75],"+":[76],"v":[77,104],"\u00b7":[78,129,130,131],"\u2207xf":[79],"I(f)":[81,84],"(3)":[82],"where":[83,135],"is":[85,137],"an":[86],"integral":[87],"expression":[88],"representing":[89],"effect":[91],"collisions":[93],"on":[94],"distribution":[96],"function":[97],"f(v,":[98],"x,":[99],"t)":[100],"particle":[102],"velocities":[103],"at":[105],"position":[106],"x.":[107],"4.":[108],"Microscopic":[109],"representations":[110],"particles":[115],"obeying":[116],"Newton\u2019s":[117],"motion":[120],"m":[121],"d":[122],"xi/dt":[124],"\u2212\u2207iV":[127],"(x1,":[128],",":[132],"xN),":[133],"(4)":[134],"V":[136],"potential":[139],"energy,":[140],"Schr\u00f6dinger\u2019s":[142],"same":[146]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2016-06-24T00:00:00"}