{"id":"https://openalex.org/W2968406617","doi":"https://doi.org/10.3390/e23040439","title":"Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint","display_name":"Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint","publication_year":2021,"publication_date":"2021-04-09","ids":{"openalex":"https://openalex.org/W2968406617","doi":"https://doi.org/10.3390/e23040439","mag":"2968406617","pmid":"https://pubmed.ncbi.nlm.nih.gov/33918678"},"language":"en","primary_location":{"id":"doi:10.3390/e23040439","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23040439","pdf_url":"https://www.mdpi.com/1099-4300/23/4/439/pdf","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/4/439/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Pritam Chattopadhyay","orcid":"https://orcid.org/0000-0002-1160-3603"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pritam Chattopadhyay","raw_affiliation_strings":["Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India"],"raw_orcid":"https://orcid.org/0000-0002-1160-3603","affiliations":[{"raw_affiliation_string":"Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ayan Mitra","orcid":"https://orcid.org/0000-0002-9436-8871"},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Ayan Mitra","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-9436-8871","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Goutam Paul","orcid":"https://orcid.org/0000-0002-5160-6032"},"institutions":[{"id":"https://openalex.org/I6498739","display_name":"Indian Statistical Institute","ror":"https://ror.org/00q2w1j53","country_code":"IN","type":"education","lineage":["https://openalex.org/I6498739"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Goutam Paul","raw_affiliation_strings":["Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India"],"raw_orcid":"https://orcid.org/0000-0002-5160-6032","affiliations":[{"raw_affiliation_string":"Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India","institution_ids":["https://openalex.org/I6498739"]}]},{"author_position":"last","author":{"id":null,"display_name":"Vasilios Zarikas","orcid":"https://orcid.org/0000-0002-0419-1858"},"institutions":[{"id":"https://openalex.org/I60559429","display_name":"Nazarbayev University","ror":"https://ror.org/052bx8q98","country_code":"KZ","type":"education","lineage":["https://openalex.org/I60559429"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Vasilios Zarikas","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan"],"raw_orcid":"https://orcid.org/0000-0002-0419-1858","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Kabanbay Batyr Ave. 53, Nur-Sultan 010000, Kazakhstan","institution_ids":["https://openalex.org/I60559429"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I60559429","https://openalex.org/I6498739"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7923,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.84627984,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"23","issue":"4","first_page":"439","last_page":"439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9958000183105469,"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":0.9958000183105469,"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/T10998","display_name":"Heat Transfer and Optimization","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14363","display_name":"Optical properties and cooling technologies in crystalline materials","score":0.00019999999494757503,"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/heat-engine","display_name":"Heat engine","score":0.8184000253677368},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5583999752998352},{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.5131999850273132},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4828000068664551},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4796999990940094},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.43369999527931213},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.421999990940094},{"id":"https://openalex.org/keywords/thermodynamic-cycle","display_name":"Thermodynamic cycle","score":0.4187999963760376}],"concepts":[{"id":"https://openalex.org/C57198161","wikidata":"https://www.wikidata.org/wiki/Q178185","display_name":"Heat engine","level":2,"score":0.8184000253677368},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5583999752998352},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.5131999850273132},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4796999990940094},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46799999475479126},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42980000376701355},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.421999990940094},{"id":"https://openalex.org/C175503448","wikidata":"https://www.wikidata.org/wiki/Q75920","display_name":"Thermodynamic cycle","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C37731324","wikidata":"https://www.wikidata.org/wiki/Q5380783","display_name":"Entropic uncertainty","level":4,"score":0.3862000107765198},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32710000872612},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C50406533","wikidata":"https://www.wikidata.org/wiki/Q1452104","display_name":"Thermal efficiency","level":3,"score":0.2935999929904938},{"id":"https://openalex.org/C163011139","wikidata":"https://www.wikidata.org/wiki/Q3932934","display_name":"Engine efficiency","level":4,"score":0.2883000075817108},{"id":"https://openalex.org/C138549593","wikidata":"https://www.wikidata.org/wiki/Q8034634","display_name":"Work output","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C34829970","wikidata":"https://www.wikidata.org/wiki/Q845260","display_name":"Quantum statistical mechanics","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2727000117301941},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2694000005722046},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C119104473","wikidata":"https://www.wikidata.org/wiki/Q188910","display_name":"Carnot cycle","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C2776897741","wikidata":"https://www.wikidata.org/wiki/Q12212546","display_name":"Quantum thermodynamics","level":3,"score":0.2563999891281128}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e23040439","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23040439","pdf_url":"https://www.mdpi.com/1099-4300/23/4/439/pdf","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:33918678","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33918678","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:arXiv.org:1908.06804","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.06804","pdf_url":"https://arxiv.org/pdf/1908.06804","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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:doaj.org/article:157e58645dca4d44ade8a5959b60b669","is_oa":true,"landing_page_url":"https://doaj.org/article/157e58645dca4d44ade8a5959b60b669","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 23, Iss 4, p 439 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/4/439/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23040439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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; Volume 23; Issue 4; Pages: 439","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8068911","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8068911","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/e23040439","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23040439","pdf_url":"https://www.mdpi.com/1099-4300/23/4/439/pdf","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2968406617.pdf"},"referenced_works_count":68,"referenced_works":["https://openalex.org/W51380241","https://openalex.org/W126915739","https://openalex.org/W204835608","https://openalex.org/W1525570999","https://openalex.org/W1527196429","https://openalex.org/W1574947529","https://openalex.org/W1934634809","https://openalex.org/W1964570781","https://openalex.org/W1970814175","https://openalex.org/W1970845041","https://openalex.org/W1976759579","https://openalex.org/W1979634094","https://openalex.org/W1981983416","https://openalex.org/W1983584387","https://openalex.org/W2002506506","https://openalex.org/W2003146312","https://openalex.org/W2006946994","https://openalex.org/W2018147731","https://openalex.org/W2020980081","https://openalex.org/W2022487148","https://openalex.org/W2023448556","https://openalex.org/W2024436403","https://openalex.org/W2027990616","https://openalex.org/W2028179726","https://openalex.org/W2028549339","https://openalex.org/W2031451638","https://openalex.org/W2038373189","https://openalex.org/W2042530477","https://openalex.org/W2052276034","https://openalex.org/W2053848737","https://openalex.org/W2054726699","https://openalex.org/W2061359415","https://openalex.org/W2065633480","https://openalex.org/W2065967227","https://openalex.org/W2073618294","https://openalex.org/W2079992998","https://openalex.org/W2087453402","https://openalex.org/W2109246727","https://openalex.org/W2110283120","https://openalex.org/W2122464632","https://openalex.org/W2123178607","https://openalex.org/W2137964687","https://openalex.org/W2142397325","https://openalex.org/W2151642725","https://openalex.org/W2199349817","https://openalex.org/W2275209877","https://openalex.org/W2516279740","https://openalex.org/W2532441140","https://openalex.org/W2566649664","https://openalex.org/W2619071992","https://openalex.org/W2678024955","https://openalex.org/W2738817994","https://openalex.org/W2765402978","https://openalex.org/W2779605244","https://openalex.org/W2792485404","https://openalex.org/W2896982874","https://openalex.org/W2945812357","https://openalex.org/W2953492881","https://openalex.org/W2962630043","https://openalex.org/W2964340462","https://openalex.org/W2968208955","https://openalex.org/W2971475076","https://openalex.org/W3016860281","https://openalex.org/W3083241825","https://openalex.org/W3088918638","https://openalex.org/W4206216506","https://openalex.org/W6693162138","https://openalex.org/W6785812081"],"related_works":[],"abstract_inverted_index":{"Quantum":[0],"cycles":[1],"in":[2,41,111],"established":[3],"heat":[4,19,114,132],"engines":[5],"can":[6,21],"be":[7,22],"modeled":[8,23],"with":[9,24,86,108],"various":[10],"quantum":[11,48,65,113],"systems":[12],"as":[13,29],"working":[14,31],"substances.":[15],"For":[16],"example,":[17],"a":[18],"engine":[20,115,133],"an":[25],"infinite":[26],"potential":[27],"well":[28,61],"the":[30,35,44,47,51,55,64,75,80,87,96,99,112,122,128,131,135],"substance":[32],"to":[33,73,120],"determine":[34,121],"efficiency":[36,56,81,129],"and":[37,50,57,82,105,124],"work":[38,58,83],"done.":[39],"However,":[40],"this":[42],"method,":[43],"relationship":[45],"between":[46],"observables":[49],"physically":[52],"measurable":[53],"parameters-i.e.,":[54],"done-is":[59],"not":[60],"understood":[62],"from":[63],"mechanics":[66],"approach.":[67],"A":[68],"detailed":[69],"analysis":[70],"is":[71],"needed":[72],"link":[74],"thermodynamic":[76,109],"variables":[77,110],"(on":[78],"which":[79],"done":[84],"depends)":[85],"uncertainty":[88,101,136],"principle":[89],"for":[90],"better":[91],"understanding.":[92],"Here,":[93],"we":[94],"present":[95],"connection":[97],"of":[98,103,130],"sum":[100],"relation":[102],"position":[104],"momentum":[106],"operators":[107],"model.":[116],"We":[117],"are":[118],"able":[119],"upper":[123],"lower":[125],"bounds":[126],"on":[127],"through":[134],"relation.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2019-08-22T00:00:00"}