A Fluctuation-Sensitive Entropy Functional and Channel Framework withApplication to Genetic Systems

A Fluctuation-Sensitive Entropy Functional and Channel Framework withApplication to Genetic 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 A Fluctuation-Sensitive Entropy Functional and Channel Framework withApplication to Genetic Systems Jacqueline Siqueira Glasenapp This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8175602/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract Entropy and entanglement are central to quantum information, yet useful, variance-sensitive generalizations remain limited. We introduce a fluctuation-sensitive entropy-like functional G = √pq + 2pq for bi-allelic systems and show it closely approximates Shannon entropy with negligible Kullback–Leibler divergence across allele-frequency regimes. Unlike standard heterozygosity, G explicitly includes a variance term, placing it among generalized entropies in the spirit of Rényi and Tsallis while preserving interpretability for stochastic populations. To study noisy dynamics we construct a family of circulant transition matrices that act as CPTP maps and recover identity, permutation, and depolarizing channels as limiting cases, fitting naturally into the operator-sum formalism. Mapping classical fluctuation to a quantum-noise parameter, we quantify entanglement decay using Werner states and concurrence, and demonstrate that increasing fluctuation drives the entanglement–separability crossover. Independent analyses yield closely matched thresholds, gene regulatory networks (GRNs) predictability collapses near p ≈ 0.854 while entanglement vanishes near p ≈ 0.873, suggesting a narrow operational Goldilocks zone for information-preserving regulation. This formalism rigorously demonstrates that the complex channel is a realization of the Ry rotation, explicitly embedding allele frequencies as the parameters that define a fundamental quantum gate. As a case study, we apply the framework to genetic systems to illustrate its utility for analyzing diversity, decoherence, and information transfer in complex stochastic dynamics. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 09 Mar, 2026 Reviewers agreed at journal 17 Feb, 2026 Reviewers invited by journal 30 Dec, 2025 Editor assigned by journal 25 Nov, 2025 Submission checks completed at journal 25 Nov, 2025 First submitted to journal 21 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. 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-8175602","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":550376603,"identity":"9b190ede-9f27-4ca0-a4c7-3cec08c73526","order_by":0,"name":"Jacqueline Siqueira 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