Timeline for Does the act of storing information (not its erasure) locally increase entropy in Maxwell's demon's memory?
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33 events
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| Jun 7 at 9:00 | comment | added | Ján Lalinský | One way to make the system generate less entropy seems to be to have it operate at much lower temperature than the system it acts on. | |
| Jun 7 at 8:45 | comment | added | Ján Lalinský | I agree, if the computer generates less entropy than the entropy it destroys, then it works as Maxwell's demon. So it need not work thermodynamically reversibly, but the amount of entropy it generates must be small enough. | |
| Jun 7 at 3:40 | comment | added | Hypnosifl | To get a Maxwell's demon type system that can temporarily decrease the net entropy and only increases it when it periodically erases its memory, it can still be true that every logical step generates a small amount of increased entropy, provided it's also true that between erasures, this positive entropy is less than the negative entropy generated by sorting the molecules in the box. Would this count as what you mean by a thermodynamically reversible computer, or are you talking about a computer that generates no entropy per step (or is just as likely to decrease as in increase in entropy)? | |
| Jun 7 at 1:57 | comment | added | Ján Lalinský | Well I was not suggesting reversal as a robust way to do that, just that it works and the reversed microstate is allowed in mechanics. The fact we cannot reverse velocities exactly is true, but does not affect the mathematical fact that if there are $M$ microstates increasing entropy, there are $M$ different microstates decreasing it. Practical system behaving as Maxwell's demon would be robust, because of the definition - Maxwell's demon is such. But I don't think just informationally/logically reversible computer will do, it has to be thermodynamically reversible, which we can't do. | |
| Jun 7 at 1:25 | comment | added | Hypnosifl | My point is just that building a maxwell's demon like system with reversible computing may allow a more robust way of temporarily reducing entropy (before its memory fills up and needs to be erased), unlike the method of trying to reverse all velocities of gas molecules which I suspect would be extremely unforgiving of the tiniest of errors due to the issue of sensitive dependence on initial conditions. | |
| Jun 7 at 1:21 | comment | added | Hypnosifl | Showing sensitive dependence on initial conditions involves looking at perturbations of some kind, the fact that such a small gravitational perturbation from such a distant small mass causes a divergence on short time scales suggests that in system of interacting atoms, any very small perturbation to the position of one atom will also have a slight gravitational effect that will cause divergence quickly. As to your 2nd point about reversing the microstate, my point is about small perturbations to a velocity-reversed microstate, not denying original unperturbed version will decrease in entropy. | |
| Jun 7 at 0:57 | comment | added | Ján Lalinský | > even fairly short times on human scale might require error less than Planck length I don't see why. When I have a gas expanding from small volume into a larger volume, and then choose one instant long after the expansion started (after $\delta t$ seconds), I have a microstate that when reversed, decreases entropy for long time $\Delta t$, and similarly for some neigborhood of the reversed microstate. | |
| Jun 7 at 0:39 | comment | added | Ján Lalinský | The article about billiard balls/molecules is a bad explanation of what chaos means. It explains it as great sensitivity to effect of weak external forces (e.g. the weak gravity force). But chaos is a property of classical mechanics models of many-particle systems even if the system is isolated, and thus it should be explained without using irrelevant additions such as effect of electrons on the other side of galaxy. Even without those being present, the system is still chaotic, that is, its evolution is very sensitive to initial condition. | |
| Jun 6 at 21:04 | comment | added | Hypnosifl | If a macrostate branches to several macrostates, each of which has lower entropy, then 2nd law is violated. Are there statistical formulations of the 2nd law that are about long-term trends but aren't contradicted by short-term drops in entropy? Even leaving aside exotic scenarios like Maxwell's demon or reversing momenta of all particles, for a small system occasional downward fluctuations in entropy can be reasonably probable, I know there's en.wikipedia.org/wiki/Fluctuation_theorem to quantify probabilities though I don't know what assumptions it makes about macrostates | |
| Jun 6 at 20:56 | comment | added | Hypnosifl | I'm thinking of short timescales for sensitive dependence on initial conditions in molecular collisions -- johnchilds.net/cueball.htm says "after about 50 collisions, which occur in less than a blink of an eye for molecules, not taking into account the gravitational pull of one electron at the edge of the galaxy would lead to enormous error in estimating what directions an oxygen molecule went". It may be that a "small enough" neighborhood would still decrease in entropy for any desired time, but even fairly short times on human scale might require error less than Planck length | |
| Jun 6 at 17:04 | comment | added | Ján Lalinský | If a macrostate branches to several macrostates, each of which has lower entropy, then 2nd law is violated. | |
| Jun 6 at 17:03 | comment | added | Ján Lalinský | > most will likely go back -- I don't see why this is true. If we chose a microstate that evolves towards higher entropy, most of points in its (small enough) neighborhood should do as well. Thus reversal will reverse the entropy evolution for most microstates - the reversed microstate, and also its reversed neighborhood. | |
| Jun 6 at 3:36 | comment | added | Hypnosifl | breaks another assumpton in those "proofs", like in Jaynes', that one macrostate evolves into another one reliably Does this mean that such proofs cannot be applied to chaotic systems if any of the variables use to define macrostates are ones that exhibit sensitive dependence on initial conditions? Jaynes aside, are there no derivations of the 2nd law (even as a long-term rather than short-term prediction) that allow for one macrostate to branch into several depending on the initial microstate? | |
| Jun 6 at 3:34 | comment | added | Hypnosifl | I'd think a difference with the scenario of just reversing all the velocities would be that such cases are typically very sensitive to perturbations, so that while entropy may decrease if you pick a set of microstates that are exact velocity-reversed versions of other microstates that lead to entropy increase, if you come up with a new set of microstates that are all the result of small random perturbations on the first set, most will likely go back to increasing in entropy. The state of a physical Maxwell's demon and its environment need not be hyper-sensitive to perturbations this way. | |
| Jun 6 at 0:54 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Jun 6 at 0:45 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Jun 6 at 0:39 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Jun 6 at 0:30 | comment | added | Ján Lalinský | This is all just somewhat complicated way of saying, yes, in mechanical models of thermodynamics, th. entropy can decrease. Why we do not observe it is the mystery, but I would not take this observation, howsoever reliable, as a rock solid law that must be always true, as Landauer and Bennet do, to derive their claims about entropy cost. It might very well be that Maxwell's demon can be constructed or discovered and 2nd law isn't universally valid. | |
| Jun 6 at 0:26 | comment | added | Ján Lalinský | Your idea of one region of phase space evolving to many disjoint regions, each of which has smaller th. entropy does obey the crucial assumption above about description of the initial state, but breaks another assumpton in those "proofs", like in Jaynes', that one macrostate evolves into another one reliably. If it doesn't (for example, there are many final macrostates, depending on which microstate is followed), then the proof of 2nd law does not work, and the final entropy need not be equal or higher, but it may be lower than the initial one. | |
| Jun 6 at 0:10 | comment | added | Ján Lalinský | But while it would be consistent with mechanics, we just do not observe such phenomena, or at least we think we don't, where isolated system would evolve towards state of lower th. entropy. "Proofs" of 2nd law assume the correct probability function to describe the initial macrostate is the one maximizing the information entropy under constraints of that macrostate (a smooth function with no holes, and not some oscillatory function with lower information entropy), but it is hard to motivate this assumption other than "its consequence, non-decrease of thermodynamic entropy, is what we observe". | |
| Jun 6 at 0:01 | comment | added | Ján Lalinský | @Hypnosifl In pure mechanics, we already know there is no problem with decrease of thermodynamic entropy, just reversal of velocities after observing an evolution after removing a constraint accomplishes that. The Liouville theorem thus has to be consistent with such decrease of thermodynamic entropy, and it is. This is because there can be complicated oscillating function $\rho$ with many mixed-in zero regions, than on evolution becomes even more dense oscillating function with differently positioned zero regions, so net volume of the phase space with non-zero probabiblity remains constant. | |
| Jun 5 at 15:11 | comment | added | Hypnosifl | In particular we might define macrostates by temperature on each side of barrier (or total particle number/energy on each side) and by the state of the demon's memory, then we'd start in a macrostate with more uniform temp on both sides and blank memory, that can evolve into a number of different macrostates that each have different sequences of 1's and 0's in memory along with less uniform temperature, such that each of those later macrostates has smaller volume in phase space than initial macrostate, but sum of their volumes is greater than or equal to initial one. | |
| Jun 5 at 15:07 | comment | added | Hypnosifl | One key principle in deriving the second law is Liouville's theorem that roughly says dynamics should preserve volume in phase space--thinking in these terms might we say that there is no problem with reliable temporary reductions in entropy, it just requires dividing phase space into macrostates in such a way that initial macrostate with volume V reliably evolves into one of several later macrostates with volumes v1, v2, ..., vN that are individually smaller than V, but collectively sum to be greater than or equal to V? | |
| Dec 7, 2020 at 17:18 | comment | added | pwf | Even if one accepts Landauer's principle, there is the additional problem that no one has shown that erasure produces enough entropy in a general Maxwell's demon to make up for the entropy decrease of the system. | |
| Dec 5, 2020 at 19:46 | comment | added | Ján Lalinský | They are different concepts with different uses. In special cases thermodynamic entropy function of state variables can be found through information entropy, but information entropy has uses beyond thermodynamics. | |
| Dec 5, 2020 at 15:27 | vote | accept | SRS | ||
| Dec 5, 2020 at 15:13 | comment | added | PrawwarP | @Lalinsky [1] begs to my mind the question as to whether information-theoretic entropy or thermodynamic entropy is more fundamental? (I would have made this into a separate question but I wanted your take on it.) | |
| Dec 5, 2020 at 15:01 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Dec 5, 2020 at 14:52 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Dec 5, 2020 at 14:33 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Dec 5, 2020 at 14:11 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Dec 5, 2020 at 13:45 | history | edited | Ján Lalinský | CC BY-SA 4.0 |
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| Dec 5, 2020 at 13:39 | history | answered | Ján Lalinský | CC BY-SA 4.0 |