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(PDF) Entropy Dynamics Associated with Self-Organization
<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="tCQMRFBPJXynbB3Epz98EjCZpQhhv4XwlYXmq1l-veVx9srPs13KFOX7Zqd1JXsW1jH58qkbNtJBOwf-D1mVlA" /> <meta name="citation_title" content="Entropy Dynamics Associated with Self-Organization" /> <meta name="citation_author" content="Rashid I Zainetdinov" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/21704682/Entropy_Dynamics_Associated_with_Self_Organization" /> <meta name="twitter:title" content="Entropy Dynamics Associated with Self-Organization" /> <meta name="twitter:description" content="A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect" /> <meta name="twitter:image" content="https://0.academia-photos.com/140676/37306/34269/s200_rashid.zaynetdinov.jpg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/21704682/Entropy_Dynamics_Associated_with_Self_Organization" /> <meta property="og:title" content="Entropy Dynamics Associated with Self-Organization" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect" /> <meta property="article:author" content="https://miit.academia.edu/RashidZaynetdinov" /> <meta name="description" content="A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect" /> <title>(PDF) Entropy Dynamics Associated with Self-Organization</title> <link rel="canonical" href="https://www.academia.edu/21704682/Entropy_Dynamics_Associated_with_Self_Organization" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = 'b092bf3a3df71cf13feee7c143e83a57eb6b94fb'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1739839045000); window.Aedu.timeDifference = new Date().getTime() - 1739839045000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect to random process of influences exerted upon a system. It was revealed that the open system responds to a strong change of conditions by steep growth of the informational entropy flow up to a maximum value at the critical point associated with the self-organization process. 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{"work":{"id":21704682,"created_at":"2016-02-08T15:47:18.167-08:00","from_world_paper_id":null,"updated_at":"2024-11-30T15:18:49.965-08:00","_data":{"abstract":"A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect to random process of influences exerted upon a system. It was revealed that the open system responds to a strong change of conditions by steep growth of the informational entropy flow up to a maximum value at the critical point associated with the self-organization process. An example of self-organization during elasto-plastic deformation of metal is considered.","ai_title_tag":"Entropy Dynamics in Self-Organization of Open Systems"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Entropy Dynamics Associated with Self-Organization","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [140676]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card ds-work-card--no-bottom-spacing"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":42411525,"attachmentType":"pdf"}"><img alt="First page of “Entropy Dynamics Associated with Self-Organization”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/42411525/mini_magick20190217-2186-qnwft9.png?1550455876" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Entropy Dynamics Associated with Self-Organization</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="140676" href="https://miit.academia.edu/RashidZaynetdinov"><img alt="Profile image of Rashid I Zainetdinov" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/140676/37306/34269/s65_rashid.zaynetdinov.jpg" />Rashid I Zainetdinov</a></div><div class="ds-work-card--detail"><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">15 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 21704682; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=21704682"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">A general model linking dynamics of informational entropy and the self-organization process in an open, steady-state, nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect to random process of influences exerted upon a system. It was revealed that the open system responds to a strong change of conditions by steep growth of the informational entropy flow up to a maximum value at the critical point associated with the self-organization process. 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