In April 2008 when I was trying to model metabolic scaling, I noticed an analogy to Stefan’s Law about black body radiation. The circulatory system as energy supply scaled by 4/3 when recipient animal tissue scaled by 1. Planck’s account of Boltzmann’s proof of Stefan’s Law involved 4/3 entropy analogous to the 4/3:1 ratio. In August 2008 the 4/3: 1 ratio of two systems, together with the connection to black body radiation, suggested that if the 4/3:1 applied at cosmological scales, it might account for space expanding. I thought the notion a little crazy and only made a slight allusion to the idea that the 4/3:1 ratio might result in a system receiving energy expanding in a paper on isotropy on arxiv in August 2008. When in 2012 I read a book by Yun Wang on Dark Energy, it seemed that perhaps the crazy notion I had in 2008 was worth investigating, and it seems to have been not so crazy after all. Have you had fruitful speculations?
In Surely You're Joking, Feynman wrote that for fun he modeled the wobble in a plate thrown in a Cornell cafeteria, without any thought that the exercise would be relevant. Later on he was able to use his analysis in a problem related to QED.
The so-called "entropy " doesn't exist at all.
During the process of deriving the so-called entropy, in fact, ΔQ/T can not be turned into dQ/T. That is, the so-called "entropy " doesn't exist at all.
The so-called entropy was such a concept that was derived by mistake in history.
It is well known that calculus has a definition,
any theory should follow the same principle of calculus; thermodynamics, of course, is no exception, for there's no other calculus at all, this is common sense.
Based on the definition of calculus, we know:
to the definite integral ∫T f(T)dQ, only when Q=F(T), ∫T f(T)dQ=∫T f(T)dF(T) is meaningful.
As long as Q is not a single-valued function of T, namely, Q=F( T, X, …), then,
∫T f(T)dQ=∫T f(T)dF(T, X, …) is meaningless.
1) Now, on the one hand, we all know that Q is not a single-valued function of T, this alone is enough to determine that the definite integral ∫T f(T)dQ=∫T 1/TdQ is meaningless.
2) On the other hand, In fact, Q=f(P, V, T), then
∫T 1/TdQ = ∫T 1/Tdf(T, V, P)= ∫T dF(T, V, P) is certainly meaningless. ( in ∫T , T is subscript ).
We know that dQ/T is used for the definite integral ∫T 1/TdQ, while ∫T 1/TdQ is meaningless, so, ΔQ/T can not be turned into dQ/T at all.
that is, the so-called "entropy " doesn't exist at all.
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Why did the wrong "entropy" appear ?
In summary , this was due to the following two reasons:
1) Physically, people didn't know Q=f(P, V, T).
2) Mathematically, people didn't know AΔB couldn‘t become AdB directely .
If people knew any one of them, the mistake of entropy would not happen in history.
Please read my paper and those answers of the questions related to my paper in my Projects.
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
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