The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics

The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics | 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 The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics Martin Petrásek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8367476/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Article type: Foundational Theory / Methodological Protocol. Landauer's principle establishes that erasing one bit of information requires at least \((k_B T\ln 2)\) of energy, a limit that experiments have approached but never violated [Landauer1961,Berut2012,Jun2014]. As quantum processors, mesoscopic feedback engines and neuromorphic architectures scale up, they operate in regimes where energetic efficiency, reliable information flow and proximity to reversible thermodynamic limits jointly determine performance. Existing descriptors---entropy production, Landauer bounds or power-efficiency measures---capture only isolated aspects of the problem and do not unify (i) energetic throughput, (ii) reliably used information rate and (iii) the reversible per-bit baseline from the same physical process.To address this gap, I introduce the energy--information--time (EIT) invariant:\[\tilde N_t = \frac{P}{\varepsilon_b\,\dot I},\]the first dimensionless, task-normalized metric for energetic reversibility across heterogeneous platforms. Here \((P)\) is incremental protocol power, \((\dot I)\) the reliably processed information rate and \((\varepsilon_b)\) the reversible free-energy baseline per bit. In the Landauer regime \((\varepsilon_b = k_B T\ln 2)\) and reversible operation corresponds to \((\tilde N_t\to 1)\) .The contributions of this paper are threefold: (i) a derivation of the invariant from free-energy equalities and information-theoretic relations, showing it encodes operational content not accessible through entropy production alone; (ii) a complete metrological framework for evaluating \((P)\) , \((\dot I)\) and \((\varepsilon_b)\) , including uncertainty budgets and constant- \((T)\) finite-time scaling diagnostics; and (iii) a laboratory protocol for circuit-QED (cQED) reset/feedback experiments in which the invariant can be directly measured. Published Landauer-erasure and feedback-engine results serve only as external illustrations of near-optimal regimes [Berut2012,Jun2014]; no new primary data are reported. This work therefore provides a unified invariant with a reproducible evaluation procedure designed for future experimental implementation. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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. 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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-8367476","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":592614883,"identity":"89a5d4b4-6a9e-4f60-80c4-d47ec7045dfb","order_by":0,"name":"Martin Petrásek","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYFADHsbGBx+ANBs7MaoPgLUwNxvOAGlhJl4Le5s0D4hBSItuA+/Bxx/32Nnz8xxsNrb5tU2ej5mB8cPHHNxazA7wJRsceJacOLO3sfFxbt9twzZmBmbJmdvwaeExkzhwgDnB4Dxjs3Fuz21GoBY2Zl78Wsx/HDhQb29/nrFN2rLntj0xWswYDhw4zLiBt7FNmuHH7UTCWg7zJUucOXA8ccaZg82GvQ23k9uYGZvx++V478EPFQeq7fl70h8++PHntu389uaDHz7i0cLAzIPEYWwDkw141IMAshaGPwQUj4JRMApGwYgEAPEaU9M+Hn/zAAAAAElFTkSuQmCC","orcid":"","institution":"Institute for Resonant Synthesis and Field Physics","correspondingAuthor":true,"prefix":"","firstName":"Martin","middleName":"","lastName":"Petrásek","suffix":""}],"badges":[],"createdAt":"2025-12-15 14:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8367476/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8367476/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102964409,"identity":"5ed76579-c4af-456e-beea-3ae4b64f50d8","added_by":"auto","created_at":"2026-02-19 04:22:13","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":701587,"visible":true,"origin":"","legend":"","description":"","filename":"SpringerNature5.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8367476/v1_covered_9fd53e0b-aea7-4c71-b8cb-7d710a2e5b6f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics","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":"","lastPublishedDoi":"10.21203/rs.3.rs-8367476/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8367476/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cb\u003eArticle type: Foundational Theory / Methodological Protocol.\u003c/b\u003eLandauer's principle establishes that erasing one bit of information requires at least \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((k_B T\\ln 2)\\)\u003c/span\u003e\u003c/span\u003e of energy, a limit that experiments have approached but never violated [Landauer1961,Berut2012,Jun2014]. As quantum processors, mesoscopic feedback engines and neuromorphic architectures scale up, they operate in regimes where energetic efficiency, reliable information flow and proximity to reversible thermodynamic limits jointly determine performance. Existing descriptors---entropy production, Landauer bounds or power-efficiency measures---capture only isolated aspects of the problem and do not unify (i) energetic throughput, (ii) reliably used information rate and (iii) the reversible per-bit baseline from the \u003cem\u003esame\u003c/em\u003e physical process.To address this gap, I introduce the energy--information--time (EIT) invariant:\\[\\tilde N_t = \\frac{P}{\\varepsilon_b\\,\\dot I},\\]the first dimensionless, task-normalized metric for energetic reversibility across heterogeneous platforms. Here \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((P)\\)\u003c/span\u003e\u003c/span\u003e is incremental protocol power, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\dot I)\\)\u003c/span\u003e\u003c/span\u003e the reliably processed information rate and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\varepsilon_b)\\)\u003c/span\u003e\u003c/span\u003e the reversible free-energy baseline per bit. In the Landauer regime \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\varepsilon_b = k_B T\\ln 2)\\)\u003c/span\u003e\u003c/span\u003e and reversible operation corresponds to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\tilde N_t\\to 1)\\)\u003c/span\u003e\u003c/span\u003e.The contributions of this paper are threefold: (i) a derivation of the invariant from free-energy equalities and information-theoretic relations, showing it encodes operational content not accessible through entropy production alone; (ii) a complete metrological framework for evaluating \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((P)\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\dot I)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((\\varepsilon_b)\\)\u003c/span\u003e\u003c/span\u003e, including uncertainty budgets and constant-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\((T)\\)\u003c/span\u003e\u003c/span\u003e finite-time scaling diagnostics; and (iii) a laboratory protocol for circuit-QED (cQED) reset/feedback experiments in which the invariant can be directly measured. Published Landauer-erasure and feedback-engine results serve only as external illustrations of near-optimal regimes [Berut2012,Jun2014]; no new primary data are reported. This work therefore provides a unified invariant with a reproducible evaluation procedure designed for future experimental implementation.\u003c/p\u003e","manuscriptTitle":"The dimensionless energy information time invariant as a universal benchmark for reversibility in quantum and mesoscopic thermodynamics","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-18 08:47:14","doi":"10.21203/rs.3.rs-8367476/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":"1d8dfa2e-322c-4775-896a-e5898e8d0f2b","owner":[],"postedDate":"February 18th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-18T08:47:14+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-18 08:47:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8367476","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8367476","identity":"rs-8367476","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}