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Thermodynamics and Stability of Non-Equilibrium Steady States in Open Systems

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Prague, Czech Republic
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Entropy 2019, 21(7), 704; https://doi.org/10.3390/e21070704
Received: 7 June 2019 / Revised: 12 July 2019 / Accepted: 17 July 2019 / Published: 18 July 2019
(This article belongs to the Special Issue Thermodynamic Approaches in Modern Engineering Systems)
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Abstract

Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium states in thermodynamically isolated systems. Unfortunately, the limitation to isolated systems is essential, and standard arguments are not applicable even for some very simple thermodynamically open systems. On the other hand, the nonlinear stability of thermodynamically open systems is usually investigated using the so-called energy method. The mathematical quantity that is referred to as the “energy” is, however, in most cases not linked to the energy in the physical sense of the word. Consequently, it would seem that genuine thermo-dynamical concepts are of no use in the nonlinear stability analysis of thermodynamically open systems. We show that this is not the case. In particular, we propose a construction that in the case of a simple heat conduction problem leads to a physically well-motivated Lyapunov type functional, which effectively replaces the artificial Lyapunov functional used in the standard energy method. The proposed construction seems to be general enough to be applied in complex thermomechanical settings. View Full-Text
Keywords: nonlinear stability; Lyapunov functional; thermodynamics; thermodynamically open systems nonlinear stability; Lyapunov functional; thermodynamics; thermodynamically open systems
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Bulíček, M.; Málek, J.; Průša, V. Thermodynamics and Stability of Non-Equilibrium Steady States in Open Systems. Entropy 2019, 21, 704.

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