Sonnino Giorgio, Tlidi Mustapha, Evslin Jarah
Department of Theoretical Physics and Mathematics, Université Libre de Bruxelles (ULB), Campus de la Plaine Code Postal 231, Boulevard du Triomphe, Brussels 1050, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):043101; discussion 043102. doi: 10.1103/PhysRevE.86.043101. Epub 2012 Oct 8.
In a recent paper, Phys. Rev. E 81, 041137 (2010), the author attempts to derive ten necessary conditions for the stability of dissipative fluids and plasmas. Assuming the validity of the local equilibrium principle, these criteria have been obtained solely from the first and second laws of thermodynamics. The Onsager reciprocity relations have not been invoked, and the author's results are supposed to be valid independent of the choice of the boundary conditions. In the present Comment, in agreement with the general theory established by Glansdorff-Prigogine in 1954 and 1970, we show that there is no variational principle expressing the necessary conditions for the stability of dissipative systems involving convective effects when the system is out of the Onsager region. In particular, we prove that the basic equations constituting the starting point of the analysis of the author, attempting to derive ten necessary conditions for the stability involving magnetohydrodynamical effects, are incorrect and in contradiction with the laws of the thermodynamics of irreversible processes.
在最近发表于《物理评论E》81卷，041137页（2010年）的一篇论文中，作者试图推导耗散流体和等离子体稳定性的十个必要条件。假设局部平衡原理成立，这些准则完全是从热力学第一和第二定律得出的。未调用昂萨格互易关系，并且作者的结果被认为与边界条件的选择无关而有效。在本评论中，与1954年和1970年格兰斯多夫 - 普里戈金建立的一般理论一致，我们表明，当系统处于昂萨格区域之外时，不存在表达包含对流效应的耗散系统稳定性必要条件的变分原理。特别是，我们证明了构成作者分析起点的基本方程，即试图推导包含磁流体动力学效应的稳定性的十个必要条件，是不正确的，并且与不可逆过程的热力学定律相矛盾。
