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Open AccessArticle

Irreversibility and Action of the Heat Conduction Process

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Author to whom correspondence should be addressed.
Entropy 2018, 20(3), 206;
Received: 24 January 2018 / Revised: 21 February 2018 / Accepted: 14 March 2018 / Published: 20 March 2018
(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)
Irreversibility (that is, the “one-sidedness” 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’s 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. View Full-Text
Keywords: irreversibility; heat conduction; Lyapunov function; least action principle; entransy; entropy irreversibility; heat conduction; Lyapunov function; least action principle; entransy; entropy
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Hua, Y.-C.; Zhao, T.; Guo, Z.-Y. Irreversibility and Action of the Heat Conduction Process. Entropy 2018, 20, 206.

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