Quantum-Classical Consistency of Entropy Dissipation and Convection in the High Entropy-Production Zone (HEZ) of the Corneal Stroma

Quantum-Classical Consistency of Entropy Dissipation and Convection in the High Entropy-Production Zone (HEZ) of the Corneal Stroma | 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 Quantum-Classical Consistency of Entropy Dissipation and Convection in the High Entropy-Production Zone (HEZ) of the Corneal Stroma Yasushi Sonoda This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7633016/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 The cornea maintains its transparency through the exquisite control of stromal hydration and structural order; a process traditionally explained from the perspective of classical thermodynamics. Previously, we proposed the existence of a High Entropy-Production Zone (HEZ) in the anterior corneal stroma, a region where solute and temperature gradients drive Marangoni convection, potentially leading to a convective flow within the cornea known as Inoue water migration. Here, we extend this concept into the quantum realm. Using a conceptual hybrid framework that integrates simplified classical transport modeling with the theory of open quantum systems, we reformulate stromal entropy production in terms of von Neumann entropy and quantum entropy generation. At the classical level, stromal entropy production arises from irreversible non-equilibrium transport processes; in the present framework, this classical entropy production provides the physical basis for its quantum reformulation. The HEZ is modeled as a spatially localized, dissipative quantum subsystem wherein water-collagen interactions and proton transport exhibit strong decoherence. Simulations incorporating Lindblad dynamics demonstrate that essential features previously identified at the classical level—a solute-dominant Marangoni driving force, thermal stabilization, and an optimal flow structure at a depth of 50–100μm—are conserved in the quantum formalism. This cross-scale consistency strengthens the assertion that HEZ is not merely a product of continuum modeling but a fundamental dissipative structure embedded within the corneal stroma. Our investigation suggests that entropy management via the HEZ is necessary to reconcile inevitable entropy production with the maintenance of optical transparency, thereby offering a new bridge between non-equilibrium thermodynamics, quantum biology, and clinical ophthalmology. Ophthalmology Biophysics High Entropy-Production Zone (HEZ) Corneal Stroma Entropy Dissipation Marangoni effect Marangoni Convection Quantum Decoherence Von Neumann Entropy Dissipative Structures Dissipative Decoherence Structure Open Quantum Systems Corneal Transparency 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. 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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-7633016","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":564245303,"identity":"2ed598d5-8f38-4f2a-927b-89c4884a9cbe","order_by":0,"name":"Yasushi Sonoda","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACHgjFxpBQAaSYmRtI0XIGpIWRFC2MbSCagBb59t6DD97UHJaXn5H+7MHDebXR/O1ALT8qtuHUYnDmXLLhnGOHDTfcyDE3SNx2PHfGYcYGxp4zt3Frkcgxk+ZhO8y4QSKHTSJx27HcBqAWZsY23FrkZ4C0/DtsPx/oMInEOcdy5xPSwnADqIW37XBiw40EM4nEhprcDYS0GJw5Y2w4ty89ecOZN2YSCccO5G4EajmIzy/y7T2GD958s7ad357+TPJHTV3uvPOHDz74UYHHYRDQDGMcBpMHCKkHgjoMxigYBaNgFIwCOAAAJQVer+9M8tUAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0009-6784-0323","institution":"Mejiro Dori Clinic","correspondingAuthor":true,"prefix":"","firstName":"Yasushi","middleName":"","lastName":"Sonoda","suffix":""}],"badges":[],"createdAt":"2025-09-16 17:49:01","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-7633016/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-7633016/v2","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99792547,"identity":"e052b350-7a45-4c40-bd8f-066a1fd00d05","added_by":"auto","created_at":"2026-01-08 13:22:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":564450,"visible":true,"origin":"","legend":"","description":"","filename":"QuantumClassicalConsistencyofEntropyDissipationversion2resubmitversion.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7633016/v2_covered_de9ade28-2d77-4253-bed6-bf09a2d789df.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"Quantum-Classical Consistency of Entropy Dissipation and Convection in the High Entropy-Production Zone (HEZ) of the Corneal Stroma","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":"High Entropy-Production Zone (HEZ), Corneal Stroma, Entropy Dissipation, Marangoni effect, Marangoni Convection, Quantum Decoherence, Von Neumann Entropy, Dissipative Structures, Dissipative Decoherence Structure, Open Quantum Systems, Corneal Transparency","lastPublishedDoi":"10.21203/rs.3.rs-7633016/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7633016/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe cornea maintains its transparency through the exquisite control of stromal hydration and structural order; a process traditionally explained from the perspective of classical thermodynamics. Previously, we proposed the existence of a High Entropy-Production Zone (HEZ) in the anterior corneal stroma, a region where solute and temperature gradients drive Marangoni convection, potentially leading to a convective flow within the cornea known as Inoue water migration. Here, we extend this concept into the quantum realm. Using a conceptual hybrid framework that integrates simplified classical transport modeling with the theory of open quantum systems, we reformulate stromal entropy production in terms of von Neumann entropy and quantum entropy generation. At the classical level, stromal entropy production arises from irreversible non-equilibrium transport processes; in the present framework, this classical entropy production provides the physical basis for its quantum reformulation. The HEZ is modeled as a spatially localized, dissipative quantum subsystem wherein water-collagen interactions and proton transport exhibit strong decoherence. Simulations incorporating Lindblad dynamics demonstrate that essential features previously identified at the classical level—a solute-dominant Marangoni driving force, thermal stabilization, and an optimal flow structure at a depth of 50–100μm—are conserved in the quantum formalism. This cross-scale consistency strengthens the assertion that HEZ is not merely a product of continuum modeling but a fundamental dissipative structure embedded within the corneal stroma. 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