Frame-Dependent Nature of Thermal Conductivity: A Relativistic Interpretation

Frame-Dependent Nature of Thermal Conductivity: A Relativistic Interpretation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Frame-Dependent Nature of Thermal Conductivity: A Relativistic Interpretation Imran Khan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7397666/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract This research extends the classical concept of thermal conductivity into the framework of special relativity, presenting a new relativistic formulation. In the classical case, thermal conductivity is treated as a fixed material property, but under high-speed relativistic conditions its value may vary between frames. To establish this, we begin with the classical one-dimensional heat conduction law and reformulate it in terms of mass and velocity. Using the relativistic mass relation, we then derive a general transformation between the thermal conductivity in the rest frame (𝑘) and that in the moving frame (𝑘 ′ ). The analysis shows that thermal conductivity is not invariant in the classical sense, but becomes framedependent. When the heat flow is parallel to the motion of the frame, it is always found that 𝑘 ′ > 𝑘, indicating an enhancement of conductivity in the moving frame. In contrast, when the heat flow is opposite to the motion, both possibilities— 𝑘 ′ > 𝑘 or 𝑘 > 𝑘′—can arise, depending on the heat flow velocity and the relative velocity of the frames, or equivalently, from the Lorentz factor. Thus, relativistic motion imparts a dual character to thermal conductivity that has no analogue in the classical framework. These findings suggest the necessity of a relativistic extension of Fourier’s law, which would be essential for accurate modeling of heat transfer in high-speed engineering systems, plasma physics, particle accelerators, and astrophysical processes. The study establishes that the relation between 𝑘 and 𝑘′ is not merely material-dependent, but instead emerges as a fundamental physical property governed by relativistic motion and velocity transformations. Relativistic heat conduction Relativistic mass relation Special relativity Thermal conductivity transformation Velocity-dependent conductivity Frame-dependent thermodynamics Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7397666","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":507409354,"identity":"ed24c088-39f8-44b3-b556-ac775ab63137","order_by":0,"name":"Imran Khan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYBACCQkgkQBm8jAwfABSbOykaGGcAdLCTIwWBqgWZh4QTUiL5OzmZw8e5tyTN5fuPSZt82ubPB8zA+OHjzm4tUjLHDM3SNxWbLhzzrk06dy+24ZtzAzMkjO34dYiJ5FgJpG4LYFxw40cM+ncntuMQC1szLx4taR/A2mxB2ux7LltT1CLtEQO2JZEsBaGH7cTCWqRnJFTBtKSvOHOGWPL3obbyW3MjM14/SJxI32b5M9tCbYbbvcY3vjx57bt/Pbmgx8+4tGCpJmBRYKxDcRibCBGPVgL8weGP0QqHgWjYBSMghEFANCUT3ha4QjtAAAAAElFTkSuQmCC","orcid":"","institution":"JLDEMC (Techno India, Baruipur)","correspondingAuthor":true,"prefix":"","firstName":"Imran","middleName":"","lastName":"Khan","suffix":""}],"badges":[],"createdAt":"2025-08-18 08:53:26","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7397666/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-7397666/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91437800,"identity":"46d6469f-adef-4b7b-b7e2-5cff839e07b7","added_by":"auto","created_at":"2025-09-16 13:31:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":235341,"visible":true,"origin":"","legend":"","description":"","filename":"Thermalconductivity1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7397666/v2_covered_fd7f9471-eb17-4e47-9492-518f0c609def.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Frame-Dependent Nature of Thermal Conductivity: A Relativistic Interpretation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Relativistic heat conduction, Relativistic mass relation, Special relativity, Thermal conductivity transformation, Velocity-dependent conductivity, Frame-dependent thermodynamics","lastPublishedDoi":"10.21203/rs.3.rs-7397666/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7397666/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research extends the classical concept of thermal conductivity into the framework of special relativity, presenting a new relativistic formulation. In the classical case, thermal conductivity is treated as a fixed material property, but under high-speed relativistic conditions its value may vary between frames. To establish this, we begin with the classical one-dimensional heat conduction law and reformulate it in terms of mass and velocity. Using the relativistic mass relation, we then derive a general transformation between the thermal conductivity in the rest frame (𝑘) and that in the moving frame (𝑘 ′ ).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe analysis shows that thermal conductivity is not invariant in the classical sense, but becomes framedependent. When the heat flow is parallel to the motion of the frame, it is always found that 𝑘 ′ \u0026gt; 𝑘, indicating an enhancement of conductivity in the moving frame. In contrast, when the heat flow is opposite to the motion, both possibilities— 𝑘 ′ \u0026gt; 𝑘 or 𝑘 \u0026gt; 𝑘′—can arise, depending on the heat flow velocity and the relative velocity of the frames, or equivalently, from the Lorentz factor. Thus, relativistic motion imparts a dual character to thermal conductivity that has no analogue in the classical framework.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThese findings suggest the necessity of a relativistic extension of Fourier’s law, which would be essential for accurate modeling of heat transfer in high-speed engineering systems, plasma physics, particle accelerators, and astrophysical processes. The study establishes that the relation between 𝑘 and 𝑘′ is not merely material-dependent, but instead emerges as a fundamental physical property governed by relativistic motion and velocity transformations.\u003c/p\u003e","manuscriptTitle":"Frame-Dependent Nature of Thermal Conductivity: A Relativistic Interpretation","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-09-15 18:58:34","doi":"10.21203/rs.3.rs-7397666/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":1,"date":"2025-08-29 11:05:52","doi":"10.21203/rs.3.rs-7397666/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"17ad3f2a-14c6-490c-901f-d15609165764","owner":[],"postedDate":"September 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-09-11T13:49:48+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-15 18:58:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-7397666","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7397666","identity":"rs-7397666","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}