
#73
Feb2912, 07:56 PM

PF Gold
P: 3,072





#74
Feb2912, 08:01 PM

P: 111

In case anyone is interested, I have posted an attachement of a paper on "The Gibbs Paradox" by E.T. Jaynes. It seems relevent, especially because Rap posted about particle indistinguishability. Jaynes seems to be taking a viewpoint similar to Ken G's; namely that entropy is largely related to the observers knowledge and their intent in setting up an experimental apparatus.




#75
Feb2912, 09:25 PM

P: 1,583





#76
Feb2912, 10:08 PM

P: 789

His explanation of the Gibbs paradox gives a deep insight into entropy  If you have two gases separated by a partition, and they have identical particles, then removing the partition changes nothing  the resulting gas is in equilibrium and the entropy is the sum of the entropies of the two gases when the partition was in. If they are different particles, no matter how small the difference, upon removing the partition, you have nonequilibrium, and upon equilibrium, you have a net increase in entropy  the total entropy is greater than the sum of the two original entropies and the increase is always the same. The crucial point is that if they are different but you have no experimental ability to tell you that they are different, then removing the partition changes nothing  there is no detectable disequilibrium, and no entropy change. Entropy is not only a function of the system, its a function of what you happen to know, or choose to know about the system. This is applicable to the concept of "correct Boltzmann counting", where, when you calculate the entropy of a gas assuming the particles have separate identities, you wind up with a nonextensive entropy (entropies do not add) and you have to subtract log(N!) to get the right answer. You can see that saying that the particles are distinguishable is equivalent to taking your original gas and instead of having two boxes as in the Gibbs paradox, you have N separate boxes, each containing one particle which is different in some way (i.e. its distinguishable) from every other particle. Again, as in the Gibbs paradox, the entropies will not add. But you have no experimental ability to tell you that the particles are different. Therefore, if you calculate entropy by assuming they are distinguishable, you have to subtract that log(N!) error you made by that assumption. And now entropies add up (i.e. its extensive). If you want a really good book on this subject, which goes through it carefully and clearly, giving many examples, check out "A Farewell to Entropy: Statistical Thermodynamics Based on Information" by Arieh BenNaim. 



#77
Mar112, 08:36 AM

PF Gold
P: 3,072





#78
May1212, 12:11 AM

P: 44

According to March 8, 2012 article in "Nature" (see citation below), the "idea of a connection between information and thermodynamics can can be traced back to Maxwell’s ‘demon’ " and the Landauer Principle which helped to resolve the paradox has finally been experimentally verified.
According to the Nature article, "The paradox of the apparent violation of the second law can be resolved by noting that during a full thermodynamic cycle, the memory of the demon, which is used to record the coordinates of each molecule, has to be reset to its initial state11,12 . Indeed, according to Landauer’s principle, any logically irreversible transformation of classical information is necessarily accompanied by the dissipation of at least kTln(2) of heat per lost bit (about 3 3 10221 J at room temperature (300 K)), where k is the Boltzmann constant and T is the temperature." See: Antoine Bérut, et al., "Experimental verification of Landauer’s principle linking information and thermodynamics" Nature 483, 187–189 (08 March 2012) http://phys.org/news/201203landaue...ryerased.html 



#79
May1212, 12:17 PM

P: 4,664

From JDStuple in post #74 on the possibility of a Mazwell's Demon, originally from "The Gibbs Paradox" by E.T. Jaynes:



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