I have a few questions concerning your setup. I have little knowledge on quantum information, and that may be the reason of my doubts.
Supose you start with with a large number of pairwise distinguishable quantum particles in a volume. Then you place the barrier. One can not say that, after...
Friends,
I will be way from the thread for a while. Personal things will keep me busy. I apologize if I do not answer immediately to any question regarding one of my posts.
That was my first time posting in PF, and has been interesting. I confess that I was frustrated at times. But now I have...
I was under the impression that we had agreed in this point.
Would you point out what in HPt's paper is in fault? Could you tell us what mistake has he made that lead him to reach the his conclusion ( that you disagree with) that there will be no increase in entropy?
The question of classic versus quantum becomes irrelevant considering the setup proposed by HPt, I think.
In the thougt experiment he proposed, with a large number of distinguishable quantum particles, there is no mixing entropy. Would you agree with that?
Yes. We know that including the ##1/N!## leads to an extensive entropy, and Jaynes (following Pauli) tells us that. However, he does not present the arguments based on the inclusion of the permuation term that accounts for the ignorance of what particles are in what subsystem after the barrier...
Yes. Jaynes is instrutive. However, I do not agree completely with the way he states his arguments. Maybe I misunderstand, but reading this discussion I have the impression that he argues that increase in entropy due to mixing depends on having the capability of segregating the mixed gases...
In the problem of thermal contact macroscopic variables are also changing. However you said that exchange of heat is not a violation of extensivity. Why would exchange of particles be?
I see no problem. The arguments of those authors show that there is no entropy of mixing in the classical model of particles.
They also show that you do not need to appeal to quantum mechanics to justify the inclusion of the ##1/N!## in the definition of entropy for this model. A clever...
Just to be sure.
You agree that the buckballs of HPt are quantum distinguishable particles?
Do you agree that in the setting proposed by HPt where each pair of a large number of particles is distinguishable there will be no mixing entropy?
Don't you think that your statement can be misleading...
Would you say that the fact that you don't need to evaluate the entropy means that you can't evaluate the entropy?
My problem is that I would like you to clarify if this way you count them as distinguishable is consistent with the way Ehrenfest counted them in 1920, vam Kampen counted in 1984...
What about coloids, granular systems, or a computer program that solves Hamiltonean dynamics? You can not appeal to quantum mechanics to include the ##1/N!## in the entropy of these systems.
I do not follow. What you mean by "you have to count accordingly"?
If you check the approach of Ehrenfest in 1920, vam Kampen in 1984, or Swendsen in 2009, among others, you will see that they do not treat distinguishable particles as if they were indistinguishable. They include the necessary permutation term that leads to no entropy of mixing for pairwise...
So we are in agreement regarding this. However, we are yet to agree in the origin of the ##1/N!##.
How would you square these statements with the inclusion of the #1/N!# in systems with a large number of pairwise distinguishable elements? These elements can be coloidal particles, such as...