Entropy deformation reveals monotonic tail amplification and instability signatures in gold market dynamics

Entropy deformation reveals monotonic tail amplification and instability signatures in gold market dynamics | 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 Entropy deformation reveals monotonic tail amplification and instability signatures in gold market dynamics Nam Anh Quach This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8962719/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 Extreme fluctuations in complex systems often emerge despite finite variance constraints, challenging conventional stability assumptions. Here, we investigate how entropy-driven deformation alters distributional structure and amplifies tail behavior in finite-variance systems. We demonstrate analytically that entropy perturbations induce a monotonic amplification of effective tail weight while preserving finite second moments, establishing a structural mechanism for instability without divergence. Using gold market dynamics as an empirical testbed, we show that periods of elevated systemic stress coincide with measurable entropy deformation and systematic tail amplification. The results reveal a general instability signature linking entropy structure and extreme-event sensitivity in complex financial systems. Our framework provides a reproducible, analytical, and empirical approach for detecting latent risk amplification and compound extreme-event sensitivity in finite-variance environments. Econometrics Entropy deformation Heavy-tailed distributions Extreme events Tail amplification Complex systems Financial instability Gold market dynamics Systemic risk 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-8962719","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":596636770,"identity":"9fa7bb46-a141-4390-b8c0-e2ff77c96d56","order_by":0,"name":"Nam Anh Quach","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACxgYQycP4+E8FkGZmbiBaC7MBzxmQFkbitbBJ8LYhuDiBOfvpxM+FO6wT+9vPHpCQnFcbzd8O1PKjYhtOLZY9uZulZ55JT5xxJi/BwHDb8dwZhxkbGHvO3MapxeBA7gZp3rbDiQ03eAwSErcdy20AamFmbMOj5fzbzb9BWuYDtRw4OOdY7nyCWm7kbgPbsuEGj2FjY0NN7gbCWt5us+ZtSzfeeCbHmJnh2IHcjUAtB/H65Xzu5tu8bday846fMf/NUFOXO+/84YMPflTg1gIFzDDGYTB5gJB6ZC11RCgeBaNgFIyCkQYAJ8Fh8iX1/zgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0000-7962-6695","institution":"Hong Bang International University","correspondingAuthor":true,"prefix":"","firstName":"Nam","middleName":"Anh","lastName":"Quach","suffix":""}],"badges":[],"createdAt":"2026-02-25 03:41:46","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-8962719/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8962719/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103508246,"identity":"055e97b2-abb3-4752-8059-9caf867d09af","added_by":"auto","created_at":"2026-02-26 13:47:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":822804,"visible":true,"origin":"","legend":"","description":"","filename":"Entropydeformationrevealsmonotonictailamplificationandinstabilitysignaturesingoldmarketdynamics.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8962719/v1_covered_e60a6935-1287-4c96-89aa-9cbaec00225c.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eEntropy deformation reveals monotonic tail amplification and instability signatures in gold market dynamics\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Hong Bang International 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":"Entropy deformation, Heavy-tailed distributions, Extreme events, Tail amplification, Complex systems, Financial instability, Gold market dynamics, Systemic risk","lastPublishedDoi":"10.21203/rs.3.rs-8962719/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8962719/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eExtreme fluctuations in complex systems often emerge despite finite variance constraints, challenging conventional stability assumptions. 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