Timeline for Gibbs entropy, Clausius' entropy and irreversibility
Current License: CC BY-SA 3.0
9 events
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| Feb 8, 2016 at 17:10 | comment | added | Wolpertinger | @Qwertuy About the addition to the question: I actually remember that when I read this paper a while ago I also didn't like that paragraph in the paper. I think he condensed it too much. My take on what he actually means is that $W_N log(W_N)$ doesn't change since the equations of motions are unitary. I use Jayne's ideas in an even more quantum mechanical context and there it is much easier to see (en.wikipedia.org/wiki/Von_Neumann_entropy is the equivalent to W_N). It's analogous to the case in the paper though. | |
| Feb 8, 2016 at 17:00 | comment | added | Wolpertinger | @Dimitri: that's also the way I understand it :) | |
| Feb 8, 2016 at 16:34 | comment | added | Dimitri | The article you linked to is very interesting. The canonical ensemble point of view doesn't take into account the time-reversal symmetry breaking in the information we have about the system: we know its past, but not its future. It kind of makes reasonable why the canonical description fails to account for the experimentally measured entropy. Thanks ! | |
| Feb 8, 2016 at 15:48 | comment | added | Qwertuy | I share Dimitri's concern. Furthermore, I feel there is a contradiction in Jaynes' paper. Surely that's my lack of understanding, but I'll tell you what I feel by expanding my original question. Thanks! | |
| Feb 8, 2016 at 15:48 | comment | added | Dimitri | I was thinking of a classical calculation of the variation in angle $\delta \theta$ in the speed of a particle after a collision. So maybe my misunderstanding comes from the quantum nature of the system. But still, I find it hard to believe that the fact that the particles were on the same size at time $t_0$ can affect the thermodynamics a long time after that. Or maybe it comes from these Bayesian statistics you were referring to ? | |
| Feb 8, 2016 at 15:29 | comment | added | Wolpertinger | I am not 100% sure which calculation you are talking about. In the example used in the paper they are explicitly talking about a quantum system. And the whole point of the paper is that it does make a difference. For the relation to classical systems the comment about diffusion in this paper (bayes.wustl.edu/etj/articles/cmystery.pdf) might help. | |
| Feb 8, 2016 at 14:46 | comment | added | Dimitri | You say that the statistical ensemble we use here is different, because we have prior information about the system. But do we ? In many introductory texbooks, we try to calculate the speed of a single particle after a few collisions. We can show that after a very short period of time (say 10 collisions) we completely lose the information about the speed or position of the particle. So is it reasonable to assume that we can track these "subtle" correlations ? Would it really make a measurable difference in the entropy ? | |
| Feb 8, 2016 at 14:26 | history | edited | user36790 | CC BY-SA 3.0 |
added 24 characters in body
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| Feb 8, 2016 at 14:02 | history | answered | Wolpertinger | CC BY-SA 3.0 |