Average Action Efficiency and Positive Feedback in the Coevolution of Dynamics and Structure

Average Action Efficiency and Positive Feedback in the Coevolution of Dynamics and Structure | 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 Average Action Efficiency and Positive Feedback in the Coevolution of Dynamics and Structure Georgi Georgiev This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8060790/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Self-organizing open systems, sustained by continuous fluxes between sources and sinks, convert stochastic motion into structured efficiency, yet a first-principles explanation of this transformation remains elusive. We derive the time-dependent Average Action Efficiency (AAE)—defined as events per total action—from a stochastic–dissipative least-action principle formulated within the Onsager–Machlup and Maximum Caliber path-ensemble frameworks. The resulting Lyapunov-type identity links the monotonic rise of AAE to the variance of action and to the rate of noise reduction, delineating growth, saturation, and decay regimes. Self-organization emerges from a reciprocal feedback between dynamics and structure: the stochastic dynamics concentrates trajectories around low-action paths, while the resulting structure, through the evolving feedback precision parameter β(t), modulates subsequent dynamics. This self-reinforcing coupling drives a monotonic increase of the dimensionless Average Action Efficiency α(t)=η/ t, providing a quantitative measure of organizational growth. In the deterministic limit, the theory recovers Hamilton’s Principle. The increase of AAE corresponds to a decrease in path entropy, yielding an information-theoretic complement to the Maximum Entropy Production and Prigogine–Onsager variational formalisms. The framework applies to open, stochastic, feedback-driven systems that satisfy explicit regularity conditions. In Part II, agent-based ant-foraging simulations confirm sigmoidal AAE growth, plateau formation, and robustness under perturbations. Because empirical AAE requires only event counts and integrated action, it offers a lightweight metric and design rule for feedback-controlled self-organization across physical, chemical, biological, and active-matter systems. Physical sciences/Mathematics and computing Physical sciences/Physics Self-organization Stochastic thermodynamics Least-action principle Path integrals Lyapunov functional Nonequilibrium statistical physics Dynamics Structure Open System Path entropy Maximum caliber principle Maximum Entropy Production Principle Feedback-controlled systems Active matter Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 Jan, 2026 Reviews received at journal 07 Jan, 2026 Reviews received at journal 07 Jan, 2026 Reviewers agreed at journal 18 Dec, 2025 Reviewers agreed at journal 17 Dec, 2025 Reviewers invited by journal 16 Dec, 2025 Editor assigned by journal 13 Nov, 2025 Submission checks completed at journal 13 Nov, 2025 First submitted to journal 07 Nov, 2025 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. 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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-8060790","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":562639139,"identity":"339bb8d3-b17a-4187-82de-7b6b9212b9d0","order_by":0,"name":"Georgi Georgiev","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYPACCQZ+GJMNicSvRbIByiJWCwODwQGYZkJa5P0XH3xc8ctCzvj48cefeXPu1PGx9x5g+FB2GKcWwxvPkg3P9kkYm53JMZPm3fZMgo3nXALjjHN4tMw4YybZ2CORuO1ADhsz77bDEmwSOQbMvG34tJz/BtJSv7n/OdBhMC1/8WiR5+9hk2z4IZFgAETScC2MeLQYSLAZGzY2SBjOuPHGTHLutmeSbTxnDA72nEvHbUv/4YcPG/7UyfP3pz/+8HbbHX759h7DBz/KrHHbciOBgYGxDc4/gETitAUk/QdNyygYBaNgFIwCZAAAfLJYLh8SLLkAAAAASUVORK5CYII=","orcid":"","institution":"Assumption University, Worcester, MA","correspondingAuthor":true,"prefix":"","firstName":"Georgi","middleName":"","lastName":"Georgiev","suffix":""}],"badges":[],"createdAt":"2025-11-08 02:23:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8060790/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8060790/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98636380,"identity":"5d8371e6-9f76-4b6c-84f2-bf4e35550155","added_by":"auto","created_at":"2025-12-19 17:27:58","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3637,"visible":true,"origin":"","legend":"","description":"","filename":"86529523d8564cd2a09c6251923a235b.json","url":"https://assets-eu.researchsquare.com/files/rs-8060790/v1/6a9c9548922c93288b8d83f6.json"},{"id":98636549,"identity":"5f86d0b3-9af3-4b1c-aef6-fd0a11d64574","added_by":"auto","created_at":"2025-12-19 17:28:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":485484,"visible":true,"origin":"","legend":"","description":"","filename":"gysgvggbqwqwdsffspxcvdwmfygtgyhc.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8060790/v1_covered_0b3dbe14-80f0-4e83-ba58-042223fe730d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Average Action Efficiency and Positive Feedback in the Coevolution of Dynamics and Structure","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"npj-complex","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjcomplex","sideBox":"Learn more about [npj Complexity](https://www.nature.com/npjcomplex/)","snPcode":"44260","submissionUrl":"https://submission.springernature.com/new-submission/44260/3","title":"npj Complexity","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Self-organization, Stochastic thermodynamics, Least-action principle, Path integrals, Lyapunov functional, Nonequilibrium statistical physics, Dynamics, Structure, Open System, Path entropy, Maximum caliber principle, Maximum Entropy Production Principle, Feedback-controlled systems, Active matter","lastPublishedDoi":"10.21203/rs.3.rs-8060790/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8060790/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Self-organizing open systems, sustained by continuous fluxes between sources and sinks, convert stochastic motion into structured efficiency, yet a first-principles explanation of this transformation remains elusive. We derive the time-dependent Average Action Efficiency (AAE)—defined as events per total action—from a stochastic–dissipative least-action principle formulated within the Onsager–Machlup and Maximum Caliber path-ensemble frameworks. The resulting Lyapunov-type identity links the monotonic rise of AAE to the variance of action and to the rate of noise reduction, delineating growth, saturation, and decay regimes. Self-organization emerges from a reciprocal feedback between dynamics and structure: the stochastic dynamics concentrates trajectories around low-action paths, while the resulting structure, through the evolving feedback precision parameter β(t), modulates subsequent dynamics. This self-reinforcing coupling drives a monotonic increase of the dimensionless Average Action Efficiency α(t)=η/\u003cI\u003et, providing a quantitative measure of organizational growth. In the deterministic limit, the theory recovers Hamilton’s Principle. 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