In this note it is shown how the theory of S.-A. Zhou and K. Miya can be modified to make it completely thermodynamically consistent. The theory presented here obeys both the principle of equipresence as well as Clausius-Duhem inequality in extended form. The thus derived results are identical to those of S. A. Zhou and K. Miya. It is shown that the final results depend explicitly on the choice made for the free energy functional.
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