Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems

Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems | 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 Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems Datorien L. Anderson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8888307/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 Systemic degradation in complex dynamical systems is often modeled as an inevitable thermodynamic slide toward equilibrium. However, we present evidence that this decay is fundamentally a noise-accumulation problem governed by spectral properties. Using novel pink noise generation methods, we demonstrate that structural coherence relies on the balance between "constructive entropy" (pink/1f noise) and "destructive entropy" (Gaussian/white noise). We introduce the Pink-to-White Noise Ratio (PWNR) as a quantitative metric of systemic integrity and show through computational modeling that when PWNR exceeds a critical threshold, systems undergo a phase transition from entropic decay to structural rejuvenation. Our results suggest that "aging" in complex systems is not a fixed temporal vector but a reversible accumulation of spectral incoherence, with profound implications for control theory, network resilience, and non-equilibrium thermodynamics. Computational Physics Thermodynamics and statistical mechanics 1/f noise coupled map lattice pink noise phase coherence bistable systems spectral flux PWNR nonequilibrium thermodynamics critical transitions self-organized criticality Full Text Additional Declarations The authors declare no competing interests. Supplementary Files spectralfluxdatav2.zip .npy and high precision csv files for pink flux illustrations2.zip Main figures and supplementary illustations on 1/f noise 1fcoherencescripts.zip experiment test scripts dlaapplicationsinpn.pdf Supplementary Paper for Applications 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-8888307","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":591734825,"identity":"3af2be67-263e-4805-a4b1-c37cd61934cd","order_by":0,"name":"Datorien L. Anderson","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0004-7688-6829","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Datorien","middleName":"L.","lastName":"Anderson","suffix":""}],"badges":[],"createdAt":"2026-02-15 20:37:10","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-8888307/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8888307/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102965615,"identity":"4a338962-5659-42fc-b59b-31aceb0095ba","added_by":"auto","created_at":"2026-02-19 04:32:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4303370,"visible":true,"origin":"","legend":"","description":"","filename":"dlasystemicrejuvenation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8888307/v1_covered_734639c7-cb0d-423f-a56d-905d3c951a8f.pdf"},{"id":102891364,"identity":"90767de9-f1cf-4ee1-aeea-a9326dd74273","added_by":"auto","created_at":"2026-02-18 05:01:55","extension":"zip","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4676915,"visible":true,"origin":"","legend":"\u003cp\u003e.npy and high precision csv files for pink flux\u003c/p\u003e","description":"","filename":"spectralfluxdatav2.zip","url":"https://assets-eu.researchsquare.com/files/rs-8888307/v1/b3bfd0d2a8a32396e78b48e5.zip"},{"id":102891367,"identity":"8ca89a98-1a1b-43e4-bddf-5d277704c60b","added_by":"auto","created_at":"2026-02-18 05:01:55","extension":"zip","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":12318194,"visible":true,"origin":"","legend":"\u003cp\u003eMain figures and supplementary illustations on 1/f noise\u003c/p\u003e","description":"","filename":"illustrations2.zip","url":"https://assets-eu.researchsquare.com/files/rs-8888307/v1/1c700887cedbd42c5137e8bc.zip"},{"id":102964539,"identity":"7bf26fe2-16f4-4c5c-9e5e-64f1f4334ed6","added_by":"auto","created_at":"2026-02-19 04:22:41","extension":"zip","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":11771,"visible":true,"origin":"","legend":"\u003cp\u003eexperiment test scripts\u003c/p\u003e","description":"","filename":"1fcoherencescripts.zip","url":"https://assets-eu.researchsquare.com/files/rs-8888307/v1/c1c2b2c6f8d2919228e45280.zip"},{"id":102891365,"identity":"ee979b49-1f34-41f2-b5d4-09221559e2db","added_by":"auto","created_at":"2026-02-18 05:01:55","extension":"pdf","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":8210822,"visible":true,"origin":"","legend":"\u003cp\u003eSupplementary Paper for Applications\u003c/p\u003e","description":"","filename":"dlaapplicationsinpn.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8888307/v1/303dcbcade8d0ad80a4f26b5.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003ePhase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems\u003c/p\u003e","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":"1/f noise, coupled map lattice, pink noise, phase coherence, bistable systems, spectral flux, PWNR, nonequilibrium thermodynamics, critical transitions, self-organized criticality","lastPublishedDoi":"10.21203/rs.3.rs-8888307/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8888307/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSystemic degradation in complex dynamical systems is often modeled as an inevitable thermodynamic slide toward equilibrium. However, we present evidence that this decay is fundamentally a noise-accumulation problem governed by spectral properties. Using novel pink noise generation methods, we demonstrate that structural coherence relies on the balance between \"constructive entropy\" (pink/1f noise) and \"destructive entropy\" (Gaussian/white noise). We introduce the Pink-to-White Noise Ratio (PWNR) as a quantitative metric of systemic integrity and show through computational modeling that when PWNR exceeds a critical threshold, systems undergo a phase transition from entropic decay to structural rejuvenation. Our results suggest that \"aging\" in complex systems is not a fixed temporal vector but a reversible accumulation of spectral incoherence, with profound implications for control theory, network resilience, and non-equilibrium thermodynamics.\u003c/p\u003e","manuscriptTitle":"Phase Coherence, Not Spectral Slope, Determines Recovery in Noise-Driven Bistable Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-18 05:01:50","doi":"10.21203/rs.3.rs-8888307/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":"0aefec0a-0554-495a-8345-70f7d5ac61bb","owner":[],"postedDate":"February 18th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62965439,"name":"Computational Physics"},{"id":62965440,"name":"Thermodynamics and statistical mechanics"}],"tags":[],"updatedAt":"2026-02-18T05:01:50+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-18 05:01:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8888307","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8888307","identity":"rs-8888307","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}