{"id":"https://openalex.org/W4395453925","doi":"https://doi.org/10.3390/e26050359","title":"Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium","display_name":"Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium","publication_year":2024,"publication_date":"2024-04-25","ids":{"openalex":"https://openalex.org/W4395453925","doi":"https://doi.org/10.3390/e26050359","pmid":"https://pubmed.ncbi.nlm.nih.gov/38785608"},"language":"en","primary_location":{"id":"doi:10.3390/e26050359","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050359","pdf_url":"https://www.mdpi.com/1099-4300/26/5/359/pdf?version=1714035737","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/5/359/pdf?version=1714035737","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036610612","display_name":"Andrea Roberto Insinga","orcid":"https://orcid.org/0000-0002-6981-2635"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Andrea R. Insinga","raw_affiliation_strings":["Department of Energy Conversion and Storage, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Energy Conversion and Storage, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000962676","display_name":"Bjarne Andresen","orcid":"https://orcid.org/0000-0003-2657-3424"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Bjarne Andresen","raw_affiliation_strings":["Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084207421","display_name":"Peter Salamon","orcid":"https://orcid.org/0000-0002-6274-406X"},"institutions":[{"id":"https://openalex.org/I26538001","display_name":"San Diego State University","ror":"https://ror.org/0264fdx42","country_code":"US","type":"education","lineage":["https://openalex.org/I26538001"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Salamon","raw_affiliation_strings":["Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA","Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA","institution_ids":["https://openalex.org/I26538001"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA;","institution_ids":["https://openalex.org/I26538001"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036610612"],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05589076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"5","first_page":"359","last_page":"359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":1.0,"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":1.0,"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/T12442","display_name":"Thermal Radiation and Cooling Technologies","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T12220","display_name":"Quantum Electrodynamics and Casimir Effect","score":0.996399998664856,"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6264455914497375},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.6230309009552002},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6194119453430176},{"id":"https://openalex.org/keywords/density-matrix","display_name":"Density matrix","score":0.6159698367118835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5687973499298096},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5405901670455933},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.48058319091796875},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.42371857166290283},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4208641052246094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3987477421760559},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3519213795661926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3104097247123718},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.264714777469635},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.19440457224845886},{"id":"https://openalex.org/keywords/mechanical-engineering","display_name":"Mechanical engineering","score":0.09550413489341736}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6264455914497375},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.6230309009552002},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6194119453430176},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.6159698367118835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5687973499298096},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5405901670455933},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48058319091796875},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.42371857166290283},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4208641052246094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3987477421760559},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3519213795661926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3104097247123718},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.264714777469635},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19440457224845886},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.09550413489341736},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e26050359","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050359","pdf_url":"https://www.mdpi.com/1099-4300/26/5/359/pdf?version=1714035737","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:38785608","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38785608","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:pubmedcentral.nih.gov:11119257","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11119257","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11119257/pdf/entropy-26-00359.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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"},{"id":"pmh:oai:doaj.org/article:1b8b77d4eb184843bfb865f8905f3b9e","is_oa":true,"landing_page_url":"https://doaj.org/article/1b8b77d4eb184843bfb865f8905f3b9e","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 5, p 359 (2024)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2ea63dd3-737d-4f5e-9672-51e43eed41fc","is_oa":true,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/2ea63dd3-737d-4f5e-9672-51e43eed41fc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Insinga , A R , Andresen , B & Salamon , P 2024 , ' Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium ' , Entropy , vol. 26 , no. 5 , 359 . https://doi.org/10.3390/e26050359","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/eddfb0db-0ae5-4427-89c7-94c803e87d2d","is_oa":true,"landing_page_url":"https://orbit.dtu.dk/en/publications/eddfb0db-0ae5-4427-89c7-94c803e87d2d","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"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":"Insinga , A R , Andresen , B &amp; Salamon , P 2024 , ' Computational Issues of Quantum Heat Engines with Non-Harmonic Working Medium ' , Entropy , vol. 26 , no. 5 , 359 . https://doi.org/10.3390/e26050359","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26050359","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26050359","pdf_url":"https://www.mdpi.com/1099-4300/26/5/359/pdf?version=1714035737","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4395453925.pdf","grobid_xml":"https://content.openalex.org/works/W4395453925.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1671143355","https://openalex.org/W1970879200","https://openalex.org/W1975746535","https://openalex.org/W1976759579","https://openalex.org/W1981707942","https://openalex.org/W1988641420","https://openalex.org/W1995589262","https://openalex.org/W2012041822","https://openalex.org/W2027561650","https://openalex.org/W2028710066","https://openalex.org/W2054824397","https://openalex.org/W2065212836","https://openalex.org/W2073955633","https://openalex.org/W2137310236","https://openalex.org/W2156608043","https://openalex.org/W2256655656","https://openalex.org/W2460442796","https://openalex.org/W2566649664","https://openalex.org/W2781624369","https://openalex.org/W2790861264","https://openalex.org/W2883041411","https://openalex.org/W2896982874","https://openalex.org/W2945812357","https://openalex.org/W2950941656","https://openalex.org/W2997879317","https://openalex.org/W2999428750","https://openalex.org/W3049648170","https://openalex.org/W3091852751","https://openalex.org/W3103681710","https://openalex.org/W3106530684","https://openalex.org/W3175233858","https://openalex.org/W4214536738","https://openalex.org/W4220891632","https://openalex.org/W4226128800","https://openalex.org/W4280540025","https://openalex.org/W4297324162","https://openalex.org/W4322723929","https://openalex.org/W4388440610","https://openalex.org/W6680386169"],"related_works":["https://openalex.org/W2165749285","https://openalex.org/W2062626603","https://openalex.org/W2392320810","https://openalex.org/W2078609410","https://openalex.org/W2474979212","https://openalex.org/W2387724274","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W2075972694","https://openalex.org/W2063161885"],"abstract_inverted_index":{"In":[0,27],"this":[1,31,82,111],"work,":[2],"we":[3,33,84,122,143],"lay":[4],"the":[5,9,39,48,52,66,70,75,78,94,102,125,128,138,151,162,176,196,204],"foundations":[6],"for":[7,195,206],"computing":[8],"behavior":[10],"of":[11,20,23,50,69,77,115,120,130,132,164,181,209],"a":[12,35,61,107,117,133,145,179,187],"quantum":[13,25,173,211],"heat":[14,174,212],"engine":[15],"whose":[16],"working":[17],"medium":[18],"consists":[19],"an":[21,86],"ensemble":[22,163],"non-harmonic":[24,197,210],"oscillators.":[26,165],"order":[28],"to":[29,59,92,137,147,172,193],"enable":[30],"analysis,":[32],"develop":[34],"method":[36,146],"based":[37],"on":[38,47],"Schr\u00f6dinger":[40],"picture.":[41],"We":[42],"investigate":[43],"different":[44],"possible":[45],"choices":[46],"basis":[49,62,129],"expanding":[51],"density":[53,103],"operator,":[54],"as":[55],"it":[56],"is":[57,97,154,202],"crucial":[58],"select":[60],"that":[63,89,96,127,153],"will":[64],"expedite":[65],"numerical":[67,207],"integration":[68],"time-evolution":[71],"equation":[72],"without":[73],"compromising":[74],"accuracy":[76],"computed":[79],"results.":[80],"For":[81],"purpose,":[83],"developed":[85],"estimation":[87],"technique":[88],"allows":[90],"us":[91],"quantify":[93,148],"error":[95,152],"unavoidably":[98],"introduced":[99,155],"when":[100,156],"time-evolving":[101],"matrix":[104],"expansion":[105],"over":[106],"finite-dimensional":[108],"basis.":[109],"Using":[110],"and":[112,149,184],"other":[113],"ways":[114],"evaluating":[116],"specific":[118,171],"choice":[119],"basis,":[121],"arrive":[123],"at":[124],"conclusion":[126],"eigenstates":[131],"harmonic":[134],"Hamiltonian":[135,183],"leads":[136],"best":[139],"computational":[140],"performance.":[141],"Additionally,":[142],"present":[144,200],"reduce":[150],"extracting":[157],"relevant":[158],"physical":[159],"information":[160],"about":[161],"The":[166,199],"techniques":[167],"presented":[168],"here":[169],"are":[170,190],"cycles;":[175],"coexistence":[177],"within":[178],"cycle":[180],"time-dependent":[182],"coupling":[185],"with":[186],"thermal":[188],"reservoir":[189],"particularly":[191],"complex":[192],"handle":[194],"case.":[198],"investigation":[201],"paving":[203],"way":[205],"analysis":[208],"machines.":[213]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
