If you know the basic physical insights of all the entropies, you may be able to correlate them on a common equivalency footing approximately.

For example, you are familiar with different types of weight - such as gravitational weight (in kg), statistical weight (unitless), evaluational weight (unitless), etc. Is it possible to express them on a common equivalency base exactly?

The starting point of thermodynamic logic is: 1) opposing perpetual motion. 2) The irreversibility of dynamics. Let's look at how to get Carnot efficiency = 1-T1/T2.

1.1 There are many kinds of type 2 perpetual motors, each of which is a natural phenomenon.

A) Machine A: against the irreversibility of thermodynamics (diffusion, heat conduction, friction, etc) - dynamics;

B) Machine B: Utilizing the Difference of Carnot Efficiency (Reversible Thermodynamics) - Thermodynamics

1.2 A and B belong to different disciplines. There is a parallel relationship between them and there is no logical mutual inevitability.

1.3. Logic of the Second Law of Thermodynamics:

Experience induction, deny that A machine==> B machine can not be manufactured==> All material Kano efficiency: 1-T1/T2.

1.4 The logic of the second law of thermodynamics violates the physical logic that A and B cannot be inferred from each other.

1.5 The second law of thermodynamics elevates the "irreversibility", which is in fact only a kinetic experience.

📷 Detailed discussion can be found in the following figure.

Dear P. K. Karmakar :

I think I see you point here. I'll say that we cannot put togheter all the concepts of weigh you just mentioned in a single individual theory, I cannot see actual connections between the different concepts of weight you mention ,

Regarding to Entropy , well, that is the question. In the case of Entropy how would you correlate all the Entropies in a common equivalent footing ?

You could probably fill a quite few books with discussions about this question, but I think a proper starting point would be the thermodynamic entropy. Because thermodynamics points to entropy as a measurable quantity. Indeed many thermodynamic textbooks give numbers for the molar entropy of a substance, and you can also find prescriptions on how these values change if temperature and pressure (for instance) change. To give an example 1 mole of H2 has at 298K and 1 bar of pressure an entropy of 130.684 J K-1 according to a book I have here. There is nothing mysterious about this.

I guess what confuses a lot of people is that the derivation of the fact that there is such a function as entropy is somewhat involved. But in fact it is rather straightforward, and based only on the assumption that there are no perpetual motion machines. In Carnot's time there were none, and this is still the case. There is no proof that these cannot exist, and the search does continue, in particular in the field of Maxwell Demons, where attempts are made to use equilibrium fluctuations can produce useful work. But at the moment there are none. If it is claimed that there are, the claimant should produce one or build one, and otherwise shut up.

I admit that many textbook derivations are not particularly enlightening, and Carnot's own derivation is rather flawed, but a mathematically sound derivation is possible, and leads, in a few steps to the fact that there is a state function, we now usually call entropy and denote by S. It also leads to the establishment of an absolute temperature scale (based on efficiency), and, with the third law (S=0 at T=0) to the possibility to assign a value like the one given above for hydrogen gas, or anything else for that matter. This is done by just measuring heat effects and integrating over temperature ranges, taking proper care of phase transitions. My point is that this is all well described and not controversial at all.

Note that I have not mentioned a second law or anything like that, for the moment this is irrelevant, I only want to establish that entropy is a state function (only dependent on the state of the system) and that changes in this function can be measured (and indeed are measured in many labs today).

If we could just be happy with that there would be no problem, but of course, being physicists (or something like it) we also want to calculate this quantity for any given system from scratch. This is already more complicated, and there may be some unresolved questions here. Boltzmann, who was more or less the first one who took the molecular nature of systems seriously (against much opposition by the way) gave such a prescription: calculate all possible configurations of the system ("number of microstates corresponding to a macrostate") take its logarithm, multiply by a constant (to get the correct units, note that entropy is a number J is energy, but so is T), and call that entropy. After that there were numerous other similar approaches, Gibbs should be mentioned here (ensemble theory). But what you may find lacking is a definite proof that this is indeed exactly the same as the thermodynamic entropy. This could be a point for further discussion.

Again, so far I have not mentioned the second law, because it is still not relevant here. If this thread indeed leads to some interesting contributions, I am sure it will come up. But for the moment we have: a thermodynamic entropy which is a measurable quantity, and a theoretical prescription on how to calculate it.

So far there are no different types of entropies (I am not mentioning informational entropy yet, because there is no immediate relation to the above, the connection does come up when Maxwell's demon rears its head.) There is only one entropy. The one you can measure with calorimetry related methods, and (if the connection is indeed correct) calculate it using equilibrium statistical mechanics.

To say a few words about the informational entropy. The connection came because Landauer's solution for the non existence of Maxwell's demon was that in order to destroy information (in Szilard's engine the side of the vessel where the particle is) you create entropy. This entropy worries me a lot. Suppose I take a book which has information (for instance a list of molar entropies of a number of substances), and a book with the same amount of paper and ink, but only random letters. Then I burn both books, will the first one generate more heat? Because in addition to the burning paper and ink also information is destroyed and entropy created. If the book is in Chinese I could not possibly figure out if it is random or has information content. But could I burn it and find out?

If I make a strand of DNA chemically I can just measure the heat that is generated or needed for every particular step, and that will lead me to the molar entropy of such s strand of DNA. If this strand codes for something like a peptide, will the entropy be different? How could that possibly be the case if it is only chemistry being involved?

OK I'll stop here for the moment, to see where this is going.

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.

.

.

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

It is very interesting discussion. Contributions are thankfully welcome. The common equivalent scaling laws are to be built up. Explorations are to continue.....

1. The second law of thermodynamics loses the ability of quantitative prediction.

2. Data processing method of law 2 of thermodynamics violates scientific discipline: modifying experimental data to satisfy theory

See the picture for details.

3. The second law of thermodynamics can only be called science if it reaches the same quantitative prediction ability as Newton's second law, otherwise it is pseudoscience.

Comparison of New and Old Thermodynamics

1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.

2. New thermodynamics pursues universality, two theoretical cornerstones:

2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.

2.2. Hydrostatic equilibrium: applicable to gases and liquids.

3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.

3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.

4. See Appendix Pictures and Documents for details.

Preprint In the gravitational field, the relation between the interna...