CUP-Ω∗: a covariant GKLS–Einstein–Langevin universal equation for thermodynamically consistent quantum–informational dynamics in the CUCE/Spinoza/Hilbert framework

CUP-Ω∗: a covariant GKLS–Einstein–Langevin universal equation for thermodynamically consistent quantum–informational dynamics in the CUCE/Spinoza/Hilbert framework | 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 Short Report CUP-Ω ∗ : a covariant GKLS–Einstein–Langevin universal equation for thermodynamically consistent quantum–informational dynamics in the CUCE/Spinoza/Hilbert framework Vicente Merino Gallardo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8399476/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 We formulate CUP-Ω∗ as a covariant evolution law for a quantum state functional defined on Cauchy hypersurfaces. The generator combines Tomonaga–Schwinger hypersurface dynamics with a covariant GKLS dissipator constructed from modular jump operators relative to a unified thermodynamic target state. Under explicit locality and integrability conditions, the evolution is foliation independent. Under detailed balance and primitivity assumptions, the quantum relative entropy to the target state provides a Lyapunov functional, ensuring a second-lawtype monotonicity and exponential convergence to a unique attractor. We further couple the matter dynamics to an Einstein–Langevin stochastic semiclassical gravity equation to encode stress-tensor fluctuations and back-reaction consistently. Finally, we derive falsifiable, quantitative constraints—finite-step Choi positivity, order-independence under spacelike update exchange, and monotone relative entropy decay—that can be tested in controlled open quantum platforms and interpreted as physically grounded stability principles for learning-like dynamics. Theoretical Astrophysics covariant open quantum systems quantum Markov semigroups detailed balance Tomonaga–Schwinger equation stochastic gravity information geometry thermodynamic learning 1 Full Text Additional Declarations The authors declare no competing interests. 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. 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-8399476","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":562653799,"identity":"a8039921-577c-48e2-9aaf-13377acef862","order_by":0,"name":"Vicente Merino Gallardo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYLCCBCDmZ2B8AKSYSdAi2cBs2EC8FhAwOECsFoNrh499eLjDxm7zjWT2BwwV1okNBLXcTkuekXgmLXnbjWTGBoYz6YS1SM7OMWZIbDucbHYj/2ADY9thYrTkfwZrMZ4BtIXxHxFa+KVzmEFa7AwkQFoaiNKSBnJYWoLEmceMMxKOpRsT1MImnfyY8WebjT1/ezLDhw811rIEtcAAxD0JxCoHAXtSFI+CUTAKRsEIAwC0CT49OA7hPgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-0678-5908","institution":"Finis Terrae University","correspondingAuthor":true,"prefix":"","firstName":"Vicente","middleName":"Merino","lastName":"Gallardo","suffix":""}],"badges":[],"createdAt":"2025-12-19 01:00:02","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8399476/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8399476/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98776867,"identity":"5ce17bc9-cdf3-4dae-b2c0-8a9998089936","added_by":"auto","created_at":"2025-12-22 12:23:50","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":324680,"visible":true,"origin":"","legend":"","description":"","filename":"CUPOmegaStarnpjAILaTeXmarginsfixed.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8399476/v1_covered_e0df21b9-f5eb-489a-b9d6-ff8ef66b3883.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eCUP-Ω\u003csup\u003e∗\u003c/sup\u003e: a covariant GKLS–Einstein–Langevin universal equation for thermodynamically consistent quantum–informational dynamics in the CUCE/Spinoza/Hilbert framework\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Finis Terrae University","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":"covariant open quantum systems, quantum Markov semigroups, detailed balance, Tomonaga–Schwinger equation, stochastic gravity, information geometry, thermodynamic learning 1","lastPublishedDoi":"10.21203/rs.3.rs-8399476/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8399476/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe formulate CUP-Ω∗ as a covariant evolution law for a quantum state functional defined on Cauchy hypersurfaces. 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