Talk:Fluctuation theorem

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I tagged this page "too technical" because, even though I don't have a physics degree, it should still be able to inform me as to why Loschmidt's paradox (which I could understand) isn't a problem. ~~ N (t/c) 04:21, 6 November 2005 (UTC)

I hardly understand anything either how is entropy defined in this article? What does an average over entropy production mean, since entropy is already defined by summing over the whole distribution of states. It seems that this article somehow associates an entropy to every microstate, or something like that.ThorinMuglindir 19:54, 6 November 2005 (UTC)

[edit] Theorem Assumptions: Time Reversal Symmetry

The list of assumptions required to prove the Fluctuation Theorem is very interesting (Part of the "Summary" section toward the end of the article). There was one thing that was unclear to me. Quoting the article, "In regard to the [assumption of time reversal symmetry], all the equations of motion for either classical or quantum dynamics are in fact time reversible." If I remember my physics correctly, to reverse the trajectory of a charged particle in a magnetic field, not just its velocity but also its charge must be reversed. Does that mean that a collection of charged particles in an external magnetic field will not obey the Fluctuation Theorem (and by extension the Second Law of Thermodynamics) unless they are capable of charge reversal? Or, is the assumption of time reversal symmetry somehow independent of (lack of) charge reversal? Compbiowes 00:38, 4 October 2006 (UTC)

About the magnetic field

Well, I think if you treat magnetic field as one generated by current flow or moving charges, then time reversal will also imply changing the direction of current flow, and thus reversing magnetic field too.

That's a good point. What I wonder about, though, is the time scale. If we mix classical and quantum ideas then it seems that the "current flow" can be "stuck" in a particular direction. More concretely, a permanent magnet can maintain its field for a very long time. Is it relevant to the Fluctuation Theorem that a system of charged particles in an external field generated by a permanent magnet would have to wait a long time for the field to reverse? If the system of charged particles could violate the Second Law and bring about a decrease in entropy as long as the field lasted, could this decrease in entropy then be used to regenerate the field? Compbiowes 00:50, 19 October 2006 (UTC)

As I tried to explain in an edit, reversibility means that for any system you choose, it would be possible to create a different system with different initial conditions whose evolution over time would look like a reversed movie of the first system. And the magnetic field of a permanent magnet is generated by the "spin" of the electrons, if you picture the spin in classical terms than a backwards movie would mean reversing the direction of all the spins. Even though quantum mechanics doesn't actually allow you to think of spin as an electron spinning on its axis or orbiting the nucleus, I think that substituting -t for t in the equations would mean reversing all the spins in QM as well, so the second system would look like the first but with the field pointing in the opposite direction. Hypnosifl 07:10, 20 October 2006 (UTC)

I can't add any more to this discussion myself without further study. I did email Denis Evans, though, and his unofficial answer was "We have only done a little on [the Fluctuation Theorem for systems in external magnetic fields]. What happens is that you need something slightly more complex than the time reversal map. It will all work but the mappings may be slightly different." Compbiowes 20:15, 20 October 2006 (UTC)

I've seen it stated by numerous physicists that both the laws of classical electromagnetism and the laws of quantum electrodynamics exhibit time-symmetry, meaning the fundamental equations of motion are unchanged by a reversal of which time direction you label positive and which you label negative. If you email Denis Evans about this precise question I'm sure he'll confirm, the quote above may be talking about issues related to some specific experimental setup but I doubt he's arguing that the fundamental equations governing the situation fail to exhibit time-symmetry. Hypnosifl 20:40, 20 October 2006 (UTC)

[edit] Is "time-averaged irreversible entropy production" just (change in entropy)/(time)?

I would think it's just equal to delta-S (change in entropy) divided by delta-t (the time interval), but I'd like some confirmation from an expert. If this is true, than it might help make the article slightly more accessible if this was mentioned somewhere. This would also mean that the fluctuation theorem could be restated in terms of changes in entropy, so that for any given time-interval, the ratio between (probability that entropy change is +delta-S) and (probability that entropy change is -delta-S) would be e^(delta-S). Hypnosifl 18:04, 20 October 2006 (UTC)