An information theoretic measure of softness in liquids

An information theoretic measure of softness in liquids | 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Download PDF Article An information theoretic measure of softness in liquids Tamoghna Das This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8675613/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Mutual Information (MI) between local stress and local non-affine deformation is proposed as a collective field variable quantifying the local softness of soft materials. The liquid-solid transition in a simple liquid is considered as a generic example of mechanical transformation through varying correlation between stress and deformation at the microscopic level. Probing through the new measure of softness, a liquid appears as a spatially heterogeneous medium of interacting interconnected regions of varying softness. In contrast, the soft regions shrink to isolated spots in the background of a negligible mean softness in the case of solids. In this view, the thermodynamic transition becomes purely geometric while keeping the essential mechanical information intact. Besides offering a general framework for understanding the mechanics of materials, this new approach can complement recent machine learning efforts by assigning physical meaning to their findings. Further, this collective variable can be used on the fly during material characterization as both of its ingredient variables are experimentally accessible. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics Physical sciences/Materials science/Soft materials Local stress Non-affine fluctuation Phase transition Spatial heterogeneity Information theory Mutual information Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review 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-8675613","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":589529483,"identity":"63a0c1dc-42c1-48a1-9255-437b28e90990","order_by":0,"name":"Tamoghna Das","email":"data:image/png;base64,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","orcid":"","institution":"Kanazawa University","correspondingAuthor":true,"prefix":"","firstName":"Tamoghna","middleName":"","lastName":"Das","suffix":""}],"badges":[],"createdAt":"2026-01-23 06:22:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8675613/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8675613/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102749103,"identity":"558f4a3f-f262-48f8-b216-b5f89afbb72d","added_by":"auto","created_at":"2026-02-16 09:11:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2753136,"visible":true,"origin":"","legend":"Article File","description":"","filename":"SftSpt.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8675613/v1_covered_69ac095a-33c0-4294-a280-73886429cdbe.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eAn information theoretic measure of softness in liquids\u003c/p\u003e","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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Local stress, Non-affine fluctuation, Phase transition, Spatial heterogeneity, Information theory, Mutual information","lastPublishedDoi":"10.21203/rs.3.rs-8675613/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8675613/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMutual Information (MI) between local stress and local non-affine deformation is proposed as a collective field variable quantifying the local softness of soft materials. The liquid-solid transition in a simple liquid is considered as a generic example of mechanical transformation through varying correlation between stress and deformation at the microscopic level. Probing through the new measure of softness, a liquid appears as a spatially heterogeneous medium of interacting interconnected regions of varying softness. In contrast, the soft regions shrink to isolated spots in the background of a negligible mean softness in the case of solids. In this view, the thermodynamic transition becomes purely geometric while keeping the essential mechanical information intact. Besides offering a general framework for understanding the mechanics of materials, this new approach can complement recent machine learning efforts by assigning physical meaning to their findings. Further, this collective variable can be used on the fly during material characterization as both of its ingredient variables are experimentally accessible.\u003c/p\u003e","manuscriptTitle":"An information theoretic measure of softness in liquids","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-16 05:58:32","doi":"10.21203/rs.3.rs-8675613/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-physics","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commsphys","sideBox":"Learn more about [Communications Physics](http://www.nature.com/commsphys/)","snPcode":"","submissionUrl":"","title":"Communications Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d846bb1a-d068-4e10-83f5-f841e84992e1","owner":[],"postedDate":"February 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":62978603,"name":"Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics"},{"id":62978604,"name":"Physical sciences/Materials science/Soft materials"}],"tags":[],"updatedAt":"2026-04-24T11:41:58+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-16 05:58:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8675613","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8675613","identity":"rs-8675613","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}