To see the demonstration, see Szargut and Valero delgado 's works (CIRCE Zaragoza)

Thank you, Philippe

please, could you be a bit more precise? I read various materials by the above authors, and by Sciubba and others, but I never found the Clausius inequality applied to capital, labor, material fluxes etcetera.All what I read extend the concept of exergy and bypass the dQ/T issue.

If you consider the second principe of thermodynamic; theoretically, the variation of entropy in a isolate system is positive or equal to zero, but never negative. This concept is true in geochemical systems ( my field of works) but I think that this concept can be analysed in specific systems. I 'll look at this relation and I 'll provide you some explanations.

The “maximal entropy” rule was explained by Boltzmann: an isolated system will try to reach the most probable state, i.e., the state with the largest number of microstates compatible with the macroscopic conditions (energy, volume, particle numbers fixed). As molecules tend to be dumb, not very individualistic, and prone to show up in large numbers, the 2nd Law of thermodynamics holds true.

If you distribute a fixed amount of energy among the molecules, they will share it randomly according to Maxwell–Boltzmann statistics.

Human beings are rather different. If you distribute a fixed amount of wealth among them, the richest will hire mercenaries and/or corrupt the government, so that they become even richer at the expense of the others. The wealth distribution in the world does not follow statistical thermodynamics!

I think the explanation of Ulrich Deiters seems logical and practical. I agree with his remarks " molecules tend to be dumb, not very individualistic, and prone to show up in large numbers, the 2nd Law of thermodynamics holds true." and "The wealth distribution in the world does not follow statistical thermodynamics!" The management is subjective while taking decisions about raw matter fluxes, useful products, by-products and waste. Some Chairmen of companies hold rights over the waste to get rich. That is life and is different from Physics!

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity

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