Second principle of thermodynamics, direction of heat flow and Fourier inequality: A comparative assessment (Q800742)

In this paper the author tries to prove that the Clausius-Planck (CP) inequality is equivalent to the total heat transfer (THT) inequality. He first claims that the Clausius-Duhem (CD) inequality does not exclude the possibility of heat to flow from colder region to hotter region; therefore, the second principle of thermodynamics should be characterized by the CP inequality rather than CD inequality. Based on this argument, the author proves the equivalence of THT-inequality to CP inequality through the use of several hypothesis proposed by the author himself. The status of the Fourier heat conduction inequality in relation to the second principle of thermodynamics is also discussed. It should be remembered that every local law has its global counterpart. CD inequality has such a correspondence while CP inequality does not. From this point of view what the author has done in this paper is nothing more than a mathematical exercise. This work might bring the discussion of the second law into scientific agenda.