Edited
I don't understand all of your formula, however, what happens if Clausius was wrong?
Take a look at this...
"The entropy of the universe tends to a maximum."
What the heck does that mean? That has got to be one of the vaguest sentences that I've ever read, lol!
And this...
"But in our nature the heat always flows from the higher temperature to the lower one and never back. In our everyday life we don't see the heat itself rises from cold to hot."
Says who? Maxwell wasn't convinced of this, and neither am I. How would Clausius have explained the spontaneous heat that is experienced by serious meditators? I have sat in motionless meditation many times and broken a sweat, and at times, the stiller I was the more intense the heat became. This is a very common phenomenon among serious practitioners of meditation. And what about a woman's hot flashes? When I was going through a chemically-induced, albeit temporary, menopause, I sure the heck spontaneously went from cold to hot! And while I can understand that Clausius may have never experienced either one of these examples, was the man never sexually turned on? They don't call it the 'heat of passion' for nothing, lol!
And then I also found this...
"A more bitter dispute between Tait and Clausius began in 1872 when Maxwell published Theory of Heat. Clausius stated that the British were trying to claim more than they deserved for the theory of heat which, Clausius said, he alone was the discoverer. One would have to add that Maxwell had, over a number of years, fully recognised Clausius's contribution, so he had little grounds for the complaint. The sadness of the situation was the effect that Clausius's attitude had on his own achievements. Daub writes in [1]:-
"Clausius's great legacy to physics is undoubtedly his idea of the irreversible increase in entropy, and yet we find no indication of interest in Josiah Gibbs' work on chemical equilibrium or Boltzmann's views on thermodynamics and probability, both of which were utterly dependent on his idea. It is strange that he himself showed no inclination to seek a molecular understanding of irreversible entropy or to find further applications of the idea; it is stranger yet, and even tragic, that he expressed no concern for the work of his contemporaries who were accomplishing those very tasks.""
http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Clausius.html
That sure doesn't sound like someone who was very interested in discovering some of the most basic laws of the universe to me, lol! How about you?