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In a recent paper, Phys. Rev E 81, 041137 (2010), the author attempts toderive ten necessary conditions for stability of dissipative fluids andplasmas. Assuming the validity of the local equilibrium principle, thesecriteria have been obtained solely from the first and the second laws ofthermodynamics. The Onsager reciprocity relations have not been invoked andauthor's results are supposed to be valid independently of the choice of theboundary conditions. In the present paper, in agreement with the general theoryestablished by Glansdorff-Prigogine in 1954 and 1970, we shall show that thereis no variational principle expressing the necessary conditions for stabilityof dissipative systems involving convective effects when the system is out ofthe Onsager region. In particular, we shall prove that the basic equationsconstituting the starting point of the analysis of the author, attempting toderive ten necessary conditions for the stability involvingmagneto-hydrodynamical effects, are incorrect and in contradiction with thelaws of the thermodynamics of irreversible processes.

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