Response-Normalized Thermodynamic Organization in Three-Dimensional Topological Collectives

Response-Normalized Thermodynamic Organization in Three-Dimensional Topological Collectives | 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 Article Response-Normalized Thermodynamic Organization in Three-Dimensional Topological Collectives Zhanpeng Jing This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9410668/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 Biological collectives often exhibit strong collective responsiveness, yet sustaining such responsiveness is a nonequilibrium activity and therefore incurs dissipative cost. This raises a central physical question: what organizes a collective system—maximal order, maximal response, or a balance between response and cost? Here we develop and test a three-dimensional responsecost framework for topological collectives. Using a three-dimensional self-propelled-particle model with topological interactions, we show that the collective is constrained by two opposing dynamical failures. At low noise, the system remains highly ordered but undergoes slow structural renewal and dynamical arrest, suppressing effective responsiveness over finite observational timescales. At high noise, coherence is lost and collective response degrades again. Between these limits, the response-normalized cost J = ˙Sproxy/χ, where ˙Sproxy is a model-consistent alignment-field dissipation proxy and χ is a susceptibility-like response measure, develops a robust interior minimum. This optimum is not pushed to arbitrarily large interaction degree; instead, it is organized within a low-degree interaction window, with a low-degree thermodynamic core and a neighboring robustness shoulder at slightly larger degree. We further show that this response-efficient optimum is robust to observable definition and that topological interactions realize it more sharply and more stably than matched metric controls. Finally, a reconstructed three-dimensional flock event provides a conservative empirical regime-level anchor: the real system occupies a highly polarized, strongly correlated collective state consistent with the model’s response-efficient regime, although the present single-event, two-frame dataset does not by itself resolve the effective interaction window. Together, these results recast collective near-critical organization not as the maximization of order alone, but as the emergence of a low-degree response-efficient regime stabilized between low-noise arrest and high-noise decoherence. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Thermodynamics Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Phase transitions and critical phenomena Full Text Additional Declarations There is NO Competing Interest. 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. 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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-9410668","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":637058872,"identity":"ccc91a2f-6f86-483a-b323-3cb387efdc32","order_by":0,"name":"Zhanpeng Jing","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYBACxmYGBuYfFf/l7O8/PgDkS8gQp4XhDLMxw4G0BJAWHqJsYmZsY05sOJBjAOIQ1sLcznv4dWEbG2Njw5nPr27UWPAwsB8+ugG/w/jSrGec42FmZuzdZp1zDOgwnrS0G/i18JgZ8JRJsLEx824zzmEDapHgMSNCC5sBDw8bzzPjnH/EaTF+zNOWICHBw8P8OLeNSFsYZ5w5YGAgwWbGnNsnAbSNgF8M+88Yf/hQcaB+gwTz48853+rk+NkPH8OvpYGBTQLKhjDY8CkHAXlg1HyAsuGMUTAKRsEoGAUoAACw7EOJ7M2GYgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0007-2823-6647","institution":"Department of Mathematics, Northeastern University","correspondingAuthor":true,"prefix":"","firstName":"Zhanpeng","middleName":"","lastName":"Jing","suffix":""}],"badges":[],"createdAt":"2026-04-14 05:20:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9410668/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9410668/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":109087367,"identity":"661080ac-ee0d-44fe-ae92-c20d8b0a6318","added_by":"auto","created_at":"2026-05-12 13:14:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4030959,"visible":true,"origin":"","legend":"Article File","description":"","filename":"008.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9410668/v1_covered_08f6dba2-dd1c-456e-ba90-81a45c9e5af3.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Response-Normalized Thermodynamic Organization in Three-Dimensional Topological Collectives","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-9410668/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9410668/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBiological collectives often exhibit strong collective responsiveness, yet sustaining such responsiveness is a nonequilibrium activity and therefore incurs dissipative cost. 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