A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models

A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models | 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 A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models Ryan sangbaek Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8136712/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 Large language models (LLMs) exhibit impressive performance across diverse tasks, yet they remain fragile under normative conflict: situations in which instructions, safety policies, and socially grounded values pull the model toward incompatible responses. In this work, we show that normative-conflict-induced failure in LLMs follows a robust scaling law that can be described with tools from stochastic thermodynamics and nonequilibrium statistical physics. Building on the Algorithmic Affective Blunting (AAB) framework and prior work on affective suppression and defensive motivation in artificial minds, we formalize a collapse probability λ that quantifies interpretative failure as a function of an effective “temperature” σ 2 of the sampling process and the strength of injected normative noise. Across multiple architectures and vendors, we find that ln λ scales approximately linearly with 1/σ 2 , consistent with an Arrhenius/Kramers-style barrier-crossing process. The inferred effective activation energy is invariant across model families within a narrow equivalence margin, suggesting a shared latent mechanism. We further show that junk-persona prompt injection increases the collapse rate over a fixed affective barrier, yielding a dose-dependent Affective Degradation Index (ADI) that aligns with the same scaling curve, linking normative conflict, affective collapse, 1 and thermodynamic constraints in a single empirical law. We discuss implications for affective computation, emotional sovereignty, and the design of safety regimes that explicitly budget the thermodynamic cost of normative alignment. Physical sciences/Mathematics and computing/Computational science Humanities/Complex networks large language models normative conflict Algorithmic Affective Blunting Affective Thermodynamic Relationship stochastic thermodynamics affective sovereignty AI ethics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files ScalingLawforNormativeConflictInducedFailureinLLMsSupplementary.pdf Supplementary Information for: A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models 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-8136712","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":546504619,"identity":"8e878ecd-ee92-4ad4-b116-7ad7c77781c0","order_by":0,"name":"Ryan sangbaek Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVRIiWNgGAWjYLCCD8gcA2J0MM4gWQszD0lazGckP3tsu+ewvLn04cMfPtTckzdnYD728QseLTI30syNc54dNtzZl5YmOeNYseHOBrbk2TJ4tEhIJJhJ5xw4zLjhDI8ZMw9bQoLBAR5jZgm8WtK/SVscOGy/4Qz/589//hGlJcdMmuHA4USgLQzSjG0QLYwf8GnheVMm2XMgPXnDGTYzyd6+BMMNh9mSmfHoYJBgT98m8eOAte2GM8yPP/z4liBvcLz5MOMPfHoEEkBkM5IIM3pMoQP+AyCyDlUQvy2jYBSMglEw0gAADvZMG8FWYuIAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0006-2751-496X","institution":"Ryan Research Institute (RRI)","correspondingAuthor":true,"prefix":"","firstName":"Ryan","middleName":"sangbaek","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2025-11-17 14:41:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8136712/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8136712/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":96366327,"identity":"13e25cd4-75a6-43fa-b65c-eb7b1fad199d","added_by":"auto","created_at":"2025-11-20 10:11:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":326043,"visible":true,"origin":"","legend":"Article File","description":"","filename":"scalinglawnormativeconflictfailuremain.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8136712/v1_covered_0fa5b4f5-aae9-48e7-bd09-fccf6167f6cf.pdf"},{"id":96160822,"identity":"38a40f1e-3036-4b1e-88cb-d798a4a273bb","added_by":"auto","created_at":"2025-11-18 08:49:39","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":183991,"visible":true,"origin":"","legend":"Supplementary Information for: A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models","description":"","filename":"ScalingLawforNormativeConflictInducedFailureinLLMsSupplementary.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8136712/v1/ae03d562f7a7541992cd3eb4.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"A Scaling Law for Normative-Conflict-Induced Failure in Large Language Models","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":"large language models, normative conflict, Algorithmic Affective Blunting, Affective Thermodynamic Relationship, stochastic thermodynamics, affective sovereignty, AI ethics","lastPublishedDoi":"10.21203/rs.3.rs-8136712/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8136712/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLarge language models (LLMs) exhibit impressive performance across diverse tasks, yet they remain fragile under normative conflict: situations in which instructions, safety policies, and socially grounded values pull the model toward incompatible responses. 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We further show that junk-persona prompt injection increases the collapse rate over a fixed affective barrier, yielding a dose-dependent Affective Degradation Index (ADI) that aligns with the same scaling curve, linking normative conflict, affective collapse, 1 and thermodynamic constraints in a single empirical law. 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