- #1
rentier
- 5
- 1
(not a paradox nowadays, but it was an issue for years)
https://en.m.wikipedia.org/wiki/Gibbs_paradox
It's not a question about a formula. I don't understand the motivation in physics to claim Gibbs mixing "paradox", the discontinuity point. What bothers the physicist to ask for a continuous transition between distinguishable and indistinguishable particles mixing (entropy).
Is it paradox that a sieve separates larger particles and smaller ones? No matter how small the difference is (in theory)? Is it paradox that 0. (real number) is different from any even the smallest number?
Either I can distinguish the particles or not. It's a binary statement/situation. Of course, it's discontinuous by definition. Two different systems; one with distinguishable particles, the other not.
Neither does it clash with the understanding of entropy as a measure of ignorance. If I can somehow differentiate particles, there is a decrease in entropy. I could (more or less laboriously) separate them and reverse the mixing.
I can't catch a logical link to the paradox.
https://en.m.wikipedia.org/wiki/Gibbs_paradox
The two gases may be arbitrarily similar, but the entropy from mixing does not disappear unless they are the same gas - a paradoxical discontinuity.
It's not a question about a formula. I don't understand the motivation in physics to claim Gibbs mixing "paradox", the discontinuity point. What bothers the physicist to ask for a continuous transition between distinguishable and indistinguishable particles mixing (entropy).
Is it paradox that a sieve separates larger particles and smaller ones? No matter how small the difference is (in theory)? Is it paradox that 0. (real number) is different from any even the smallest number?
Either I can distinguish the particles or not. It's a binary statement/situation. Of course, it's discontinuous by definition. Two different systems; one with distinguishable particles, the other not.
Neither does it clash with the understanding of entropy as a measure of ignorance. If I can somehow differentiate particles, there is a decrease in entropy. I could (more or less laboriously) separate them and reverse the mixing.
I can't catch a logical link to the paradox.