{"id":"https://openalex.org/W2042467745","doi":"https://doi.org/10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","title":"A thermodynamical approach to noise in non-linear networks","display_name":"A thermodynamical approach to noise in non-linear networks","publication_year":1998,"publication_date":"1998-03-01","ids":{"openalex":"https://openalex.org/W2042467745","doi":"https://doi.org/10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","mag":"2042467745"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","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/A5076976263","display_name":"Laurens Weiss","orcid":null},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Laurens Weiss","raw_affiliation_strings":["Department of Electrical Engineering, Otto-von-Guericke-University, Magdeburg, Germany","Department of Electrical Engineering, Otto\u2010von\u2010Guericke\u2010University, Postfach 4120, 39016 Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Otto-von-Guericke-University, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Department of Electrical Engineering, Otto\u2010von\u2010Guericke\u2010University, Postfach 4120, 39016 Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058996739","display_name":"Wolfgang Mathis","orcid":"https://orcid.org/0000-0002-7386-2870"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wolfgang Mathis","raw_affiliation_strings":["Department of Electrical Engineering, Otto-von-Guericke-University, Magdeburg, Germany","Department of Electrical Engineering, Otto-von-Guericke-University Magdeburg, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Otto-von-Guericke-University, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Department of Electrical Engineering, Otto-von-Guericke-University Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076976263"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":{"value":3660,"currency":"USD","value_usd":3660},"apc_paid":null,"fwci":1.9771,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.86092205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"26","issue":"2","first_page":"147","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9973999857902527,"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":0.9973999857902527,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9769999980926514,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5934019684791565},{"id":"https://openalex.org/keywords/master-equation","display_name":"Master equation","score":0.511800229549408},{"id":"https://openalex.org/keywords/linear-map","display_name":"Linear map","score":0.506665050983429},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4962664246559143},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.48775893449783325},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48033633828163147},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.45122307538986206},{"id":"https://openalex.org/keywords/johnson\u2013nyquist-noise","display_name":"Johnson\u2013Nyquist noise","score":0.4406488537788391},{"id":"https://openalex.org/keywords/linearity","display_name":"Linearity","score":0.41761842370033264},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.41490694880485535},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26275426149368286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2543213665485382},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18029996752738953},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09519481658935547},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08979609608650208}],"concepts":[{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5934019684791565},{"id":"https://openalex.org/C128805008","wikidata":"https://www.wikidata.org/wiki/Q722878","display_name":"Master equation","level":3,"score":0.511800229549408},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.506665050983429},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4962664246559143},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.48775893449783325},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48033633828163147},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.45122307538986206},{"id":"https://openalex.org/C104419016","wikidata":"https://www.wikidata.org/wiki/Q1337490","display_name":"Johnson\u2013Nyquist noise","level":3,"score":0.4406488537788391},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.41761842370033264},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.41490694880485535},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26275426149368286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2543213665485382},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18029996752738953},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09519481658935547},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08979609608650208},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-007x(199803/04)26:2<147::aid-cta998>3.0.co;2-e","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2073801793","https://openalex.org/W1986260494","https://openalex.org/W2111360083","https://openalex.org/W2088068170","https://openalex.org/W2080994636","https://openalex.org/W2353844725","https://openalex.org/W2085911975","https://openalex.org/W2389228754","https://openalex.org/W3138373256","https://openalex.org/W1965191890"],"abstract_inverted_index":{"The":[0,147],"physical":[1],"assumptions":[2],"on":[3],"which":[4],"linear":[5],"fluctuation":[6],"theory":[7,27,127,140],"is":[8,23,86,90,122,141],"based":[9],"do":[10],"not":[11],"apply":[12,41,125],"to":[13,46,77,96,124,128,143,151],"internal":[14,29],"noise":[15,31,49,170,181],"in":[16,32,50,66],"non-linear":[17,33,52,97,101,129,157],"systems.":[18,146],"As":[19,54],"a":[20,91],"consequence,":[21],"there":[22],"still":[24],"no":[25],"complete":[26],"for":[28,71,113,156],"(thermal)":[30],"electrical":[34,84],"networks.":[35],"In":[36,159],"this":[37,160,162],"paper":[38,163],"the":[39,57,72,78,82,100,126,139,165,176],"authors":[40],"Stratonovich's":[42],"\u2018non-linear":[43],"non-equilibrium":[44],"thermodynamics\u2019":[45],"describe":[47],"thermal":[48],"reciprocal":[51],"RLC-networks.":[53],"an":[55],"example":[56],"(deterministic)":[58],"Brayton\u2013Moser":[59],"equations":[60,70,110],"are":[61,103,111,149],"treated.":[62],"A":[63,118],"stochastic":[64,177],"description":[65],"terms":[67],"of":[68,81,93,116,120,168,179],"master":[69,109],"one-time":[73],"probability":[74],"density":[75],"related":[76],"Markov":[79],"processes":[80],"fluctuating":[83],"quantities":[85],"obtained.":[87],"This":[88],"decription":[89],"generalization":[92],"Nyquist's":[94],"theorem":[95],"resistors.":[98,158],"When":[99],"resistances":[102],"represented":[104],"by":[105],"Taylor":[106],"polynomials,":[107],"different":[108,114],"obtained":[112],"degrees":[115],"non-linearity.":[117],"transformation":[119],"variables":[121],"used":[123,150],"dynamical":[130],"network":[131],"elements.":[132],"To":[133],"consider":[134],"networks":[135],"including":[136],"independent":[137],"sources,":[138],"enlarged":[142],"open":[144],"thermodynamical":[145],"results":[148],"derive":[152],"approximate":[153,166],"noise-equivalent":[154],"circuits":[155],"sense,":[161],"proves":[164],"validity":[167],"\u2018conventional\u2019":[169],"source":[171],"models":[172],"and":[173],"explicitly":[174],"fixes":[175],"properties":[178],"these":[180],"sources":[182],"(as":[183],"far":[184],"as":[185],"possible).":[186],"\u00a9":[187],"1998":[188],"John":[189],"Wiley":[190],"&":[191],"Sons,":[192],"Ltd.":[193]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}