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- TL;DR Summary
- There is no paradox. Gibbs made a mistake. Ehrenfest explained the entropy of mixing of distinguishble elements with the problem of the dog's fleas. However, more than a century later this fact is ignored by most.
Hi,
I recently discovered that there is no real paradox in the question of the mixing of classical distinguishble particles. I was shocked. Most books and all my professors suggest that an extensible entropy could not be defined for distinguishble particles.
I believe that many of you will be skeptical of my claim that no paradox exists. After a careful read of the Wikipedia article on the gibbs paradox I learned that there is no real paradox. Gibbs made a mistake. Van Kampen 1984, and Jaynes 1996 (two references that I found in the wikipedia page) make the point clear. Jaynes goes as far as to suggest that Gibbs was senile when he wrote about the paradox of mixing.
A 2 pages text that is right to the point is
Swendsen, R. H. (2008). Gibbs’ paradox and the definition of entropy. Entropy, 10(1), 15-18.
I would like to know if other people is surprised with that. It seems to me that because physicists are more concerned with Bose and Fermi indistinguishable particles, this misconception regarding the mixing of distinguishble elements has lingered.
I recently discovered that there is no real paradox in the question of the mixing of classical distinguishble particles. I was shocked. Most books and all my professors suggest that an extensible entropy could not be defined for distinguishble particles.
I believe that many of you will be skeptical of my claim that no paradox exists. After a careful read of the Wikipedia article on the gibbs paradox I learned that there is no real paradox. Gibbs made a mistake. Van Kampen 1984, and Jaynes 1996 (two references that I found in the wikipedia page) make the point clear. Jaynes goes as far as to suggest that Gibbs was senile when he wrote about the paradox of mixing.
A 2 pages text that is right to the point is
Swendsen, R. H. (2008). Gibbs’ paradox and the definition of entropy. Entropy, 10(1), 15-18.
I would like to know if other people is surprised with that. It seems to me that because physicists are more concerned with Bose and Fermi indistinguishable particles, this misconception regarding the mixing of distinguishble elements has lingered.