{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T03:40:58Z","timestamp":1762659658446,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T00:00:00Z","timestamp":1521504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51676108","51356001"],"award-info":[{"award-number":["51676108","51356001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Fund for Creative Research Group","award":["51621062"],"award-info":[{"award-number":["51621062"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Irreversibility (that is, the \u201cone-sidedness\u201d of time) of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy and its production rate have been generally regarded as Lyapunov functions in order to measure the irreversibility of various physical processes. In fact, the Lyapunov function is not always unique. In the represent work, a rigorous proof is given that the entransy and its dissipation rate can also serve as Lyapunov functions associated with the irreversibility of the heat conduction process without the conversion between heat and work. In addition, the variation of the entransy dissipation rate can lead to Fourier\u2019s heat conduction law, while the entropy production rate cannot. This shows that the entransy dissipation rate, rather than the entropy production rate, is the unique action for the heat conduction process, and can be used to establish the finite element method for the approximate solution of heat conduction problems and the optimization of heat transfer processes.<\/jats:p>","DOI":"10.3390\/e20030206","type":"journal-article","created":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T06:57:11Z","timestamp":1521529031000},"page":"206","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Irreversibility and Action of the Heat Conduction Process"],"prefix":"10.3390","volume":"20","author":[{"given":"Yu-Chao","family":"Hua","sequence":"first","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiao","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeng-Yuan","family":"Guo","sequence":"additional","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,20]]},"reference":[{"key":"ref_1","unstructured":"Prigogine, I. 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