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Maxwell’s Demon Continues to Startle Scientists (quantamagazine.org)
88 points by jnord 3 months ago | hide | past | favorite | 47 comments

A number of comments refer to the “supernatural” while others raise the notions of entropy, suggesting that the thought experiment is about getting something for nothing.

Even from the very early days, both notions were laughable, and both missed the point. The question has to do more with what sort of entity/agent/machine the demon would be, what its physical characteristics would be.

Since Bennett’s work of 1982, building on Landauer’s work of 1961 (both mentioned in the article), we know that the demon is an information processing machine, observing and recording state, occasionally acting, and occasionally erasing its state records.

The question is how efficient can we make the machine, how passive or active it needs to be.

Potential applications include more efficient cooling systems and advances in the theory and mathematics of information processing.

Sorry for the auto-reply, but I got thinking more deeply after writing this, and realized I missed a key point....

Maxwell’s Demon was an artful and subtle and unexpected recognition that 19th century physics and mathematics had neither concepts nor expressive capabilities to even describe what was happening.

I marvel at the intuition and cleverness involved: “here is a thing, so simple to describe, that we do not even have the rudiments necessary to explore, let alone explain”.

To take an inchoate notion of a major gap and express it so simply, so memorably, is a masterstroke.

Maxwell was - to put it mildly - a pretty bright guy.

Evaporation is pretty efficient, as a sorting device. It also doesn't involve computation. But it gets the Demon's job done.

In some older discussion [2], I linked to a 1987 article in the Scientific American [1] that explains this much more clearly, I think:

[1] https://ecee.colorado.edu/~ecen4555/SourceMaterial/DemonsEng...

(Bonus: an ad for a "letter quality daisy wheel word processor" from Brother, and one for the new Tandy 4000 ("Put a Tandy 4000 on your desk and unleash the incredible power of the 32-bit, 16-megaherz 80386 microprocessor."))

[2] https://news.ycombinator.com/item?id=22138224

Brother WP looks like it sells for ~$200 on eBay. But I think a mint Tandy 4000 would really be a museum piece ;)

Going down to the level of a quantum maxwell demon, a superconducting qubit, a single photon. One still finds measurable dissipation. An inherent non-linearity of optics in a medium. If the entire system could be constructed of light, manipulated by light energy. we could perhaps see a memory entropy lower than the systems ;)

I never understood what was so important about Maxwell's Demon. If an external, supernatural force acts upon a system to reduce entropy how is this in any way contradictory or surprising? Articles, like this one, explain the thought experiment, then are just content to assume that this is obviously a puzzle of some kind and I just think "so what?"

I think "demon" just acts as a placeholder for "component whose behavior we can describe in intentional terms." As I understand it, the demon is not supposed to be a supernatural force, it's supposed to be a physical component in the system. We know now that building such a component is theoretically impossible, which is why the demon would need to appeal to supernatural means, but this was not clear for a long time.

Besides, "Maxwell's sensor controlled opening" sounds boring.

edit: To cite Theory of Heat ( https://upload.wikimedia.org/wikipedia/commons/b/b8/J._Clerk... ):

"But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own (emphasis mine), would be able to do what is at present impossible to us. ... He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."

Which IMO makes it clear Maxwell thought of his demon as a fundamentally natural system.

>As I understand it, the demon is not supposed to be a supernatural force, it's supposed to be a physical component in the system.

if you did that, it would be obvious what the problem is with the thought experiment: physical components have entropy. moving pieces need motive force which make heat, and movement also makes heat.

the thought experiment only makes sense with a nonsense demon, because the though experiment isnt possible.

No. The paradox makes perfect sense with a technical device.

It is conceivable to have fine mechanisms that can be operated with minimal loss of energy and entropy (not bounded away from zero).

Thus, the thought experiment poses a challenge. As the article alluded to, the paradox was solved by the fact that information processing is required, which is also in theory reversible, except for the process of erasing information, which interestingly requires some minimum energy. That then would be just enough to compensate for the energy won from the demon, thus not violating the laws of thermodynamics.

The "demon" is nomenclature in parallel with Laplace's demon (a thought experiment with a machine that knows position and velocity of all particles, and thus can compute the entire past and future of the universe, in Newtonian physics).


ETA: nicklecompte says it perfectly below: https://news.ycombinator.com/item?id=26912158

Its obvious to us 150 years later because we are very familiar with the idea that processing data needs energy, its as natural an idea to us as plugging in a phone. It wasn't so obvious in 1867.

That's the thing: it doesn't!

(i.e. Processing data doesn't need energy - more correctly "work")

In the limit, you can process information adiabatically.(*) i.e. you can perform a computation without heat exchange, and you can perform computations reversibly.

Maxwell's demon as a thought experiment is actually quite a deep and subtle probe into the boundary between information and thermodynamics.

What you CAN'T do adiabatically or reversibly is clear or set bits and throw away their initial state.

In theory you could make a classical mechanical turing machine that could perform a computation for an arbitrarily small amount of work, but to prepare a blank tape for it (or to configure a tape into a known configuration) will take a certain minimal expenditure of work.

* Ignoring Quantum Physics for now

The Wikipedia page for Reversible Computing might be a place to start reading if you're interested in following up.

I don't think you give Maxwell enough credit.

Maxwell was a giant obviously but with his thought experiment of the Demon (which he quite casually came up with in a letter to a friend) he suspected that he had successfully poked holes in the second law - to "show that the 2nd Law of Thermodynamics has only statistical certainty" as he put it. So he thought the law was a statistical guide that could be gotten around in special circumstances. It took the thinkers of the time a long time to realise that tracking all the molecules would need energy.

Whereas if you re-state the thought experiment using todays technology - "imagine a device that tracks all the molecules and opens a hatch to only let the fast ones through" its obvious to us - with our modern conception of processing - that such a device would need a fair bit of juice.

Source: https://archive.org/details/lifescientificwo00knotuoft/page/...

> its obvious to us - with our modern conception of processing - that such a device would need a fair bit of juice

It wouldn't.

The hatch itself could operate with no net energy lost/gained, e.g. using a counterweight to cancel out the momentum.

Any required calculations could be carried out with a reversible computer, e.g. a billiard ball computer. This way, once our computation is finished, we just can just run it in reverse to get back any energy that was spent (e.g. anything that needed charging during the computation, will get discharged on the way back; and likewise for any lifting, pushing, etc.).

The only thing which requires energy is resetting the device. This cannot be done reversibly, since it has to 'forget' whether the hatch got opened or not; i.e. reset(opened) -> init and reset(closed) -> init, so we can't "undo" the 'reset' operation to recover any energy it used.

> it would be obvious what the problem is with the thought experiment: physical components have entropy. moving pieces need motive force which make heat, and movement also makes heat.

This is such a bad answer, on so many levels.

> physical components have entropy

But do they? It's a bit of a hand-wavey statement on its own, but even if we made it more precise it would be putting the cart before the horse. If we want to understand or explain entropy, then we can't make assertions like this; it would just lead to circular reasoning (fundamentally, our "explanations" would distill down to "physical components have entropy because physical components have entropy").

> moving pieces need motive force which make heat

This is simply incorrect. "Heat" is a large-scale, statistical phenomenon: the kinetic energy of uncorrelated internal movement of components (e.g. the molecules of a gas moving and spinning). Moving pieces don't "make heat"; pieces moving in uncorrelated ways is heat. Hence we have to focus on the correlation, which is exactly what we mean by entropy.

Also "motive force" sounds a bit hand-wavey, and possibly anthropocentric (e.g. it conjures images of bolting things to a steam engine). A better term might be energy gradient, or path of stationary action.

> movement also makes heat

No it does not. First of all, movement is relative. When cosmic rays hit the Earth, they measure Earth's movement as being close to the speed of light. A ballistic missile at apogee measure's the Earth's movement as zero. This is consistent, since movement is relative. Yet heat is not relative: there is no "heat dilation", since heat has net-zero movement in all directions (net movement is correlated and hence, by definition, not heat). Both the cosmic ray and the missile must measure the Earth's heat as the same; hence heat cannot depend on movement.

Secondly 'conservative forces' like gravity and electromagnetism do not lose energy: they can cause perpetual motion; especially at the atomic scale and below, where non-conservative pseudo-forces like friction don't play a role. This is the scale of Maxwell's Demon.

Your faulty reasoning has also arrived at the wrong conclusion. Maxwell's Demon (or a physical analogue, like a nanomachine) can separate gas into hot and cold compartments, without causing any heat, without the need of any external 'motive force', in a conservative/reversible way.

If we follow the correct line of reasoning (which took 115 years to discover, as the article mentions!) we find the catch: it would require unlimited memory. That's something that's not at all "obvious", and certainly not clear from a treatment of 'motive forces' and 'heat'.

Which, I believe, was literally the point of the experiment - proof by contradiction.

In modern terms, we would use the word "oracle" instead of "demon."

Not necessarily. Our computers have dozens of things we call "daemons" running in the background and nobody considers them supernatural.

The word "daemon" for a computer program was inspired by Maxwell's demon, because it works tirelessly in the background. http://www.takeourword.com/TOW146/page4.html

It is indeed obvious that an external force can apply energy to a system to reduce entropy.

The trick is that, if you ignore the thermodynamics of information processing, Maxwell's demon can work with arbitrarily little energy (the only physical work it is doing is opening/closing a door with arbitrarily little mass). In fact Maxwell's demon can perform any amount of thermodynamic work with essentially zero physical work. It really does seem to be a violation of energy conservation.

The only way to solve this is by considering the thermodynamics of Maxwell's demon's brain (creating and destroying state as it determines whether or not to let a given molecule pass the door) - and in particular understanding that there is a fundamental thermodynamic cost to storing or deleting information, it is not just a consequence of imperfect circuit/neuron design.

The demon is introduced as a magical effect, but the obvious followup question is why can't you actually implement it. Why can't you make a machine that lowers entropy by opening and closing a door to let atoms go one way but not the other? Why can't you make a one-way valve? What specifically is magical about the demon? There is an important insight hiding inside that demon.

The demon is not really supposed to be magical, but instead "some physical process or machine", e.g. a future nanomachine or something. It's like a "perpetual motion machine" - a hypothetical object that can be used in thought experiments. If it could be shown that creating a Maxwell's demon that creates less entropy than it reduces is impossible, then the paradox is solved. A [brownian ratchet](https://en.wikipedia.org/wiki/Brownian_ratchet) is an example of a (failed) implementation.

What’s magical: it can observe, decide, and act with zero energy (or at least less energy than real-world thermodynamics requires).

> observe

This isn't magical: it's just entanglement/causality. If "observing" required energy, then atoms would either blow apart (due to their electrons not "observing" their nuclei), or collapse (due to their electrons losing energy by "observing" their nuclei).

> decide

This isn't magical: https://en.wikipedia.org/wiki/Billiard-ball_computer

> act

This isn't magical: https://en.wikipedia.org/wiki/Conservative_force

I think the point is that it's not "supernatural". Conceptually you could implement it. The opening and closing involves zero work. In reality the work won't be zero due to friction, but you can in principle at least approximate it really well.

> The opening and closing involves zero work


It can be done conservatively https://en.wikipedia.org/wiki/Conservative_force

The work will never be zero, and I have a hunch it could well be greater than your overall temperature gain.

If the opening works on non-charged particles, it has to have mass and opening and closing it is not possible without work.

The work might be tiny, but your temperature gain is probably event tinier.

If the particle is charged, you don't need a physical gate, but you do work on the particle by exerting a force on it.

You also somehow must detect the particle, and that also takes energy.

> If the opening works on non-charged particles, it has to have mass and opening and closing it is not possible without work.

You could open the gate by pulling it up, which would require work, but you could recover the entire work by letting it sink down again.

It has been shown that the solution was not the physical work of opening/closing the gate, but the work required in information processing, in particular deleting information.

Reducing it to something absurd, is it anything beyond "If we just ignore this one rule of physics, this other rule of physics also stops working. Gotcha!"?

I think the real trick with the thought experiment is: which law of physics is the Demon ignoring?

The answer (spoilers) is that the demon is ignoring the entropy of the information it must learns about the particles that pass through the gate - either the Demon stores info about which particles are let through, which has entropy of its own, or the Demon erases that data, which comes with an energy cost that must subtly heat something up and again increases entropy elsewhere. Either way, the entropy of the total system still increases, even though the entropy of the gas decreases.

I would have thought that the laws of entropy would continue to exist, even once this thought experiment plays out.

Sure, once the particles have been divided, the difference between the hottest and coldest particles in each room would be reduced; but why wouldn't the scale of temperatures not subdivide to infinity?

The bounds of each universe have changed - but why _wouldn't_ the same laws continue?

The "laws of entropy" are about the observer's uncertainty about the physical state which is then described as a thermodynamical system (in equilibrium in the classical formulation). And they can be “violated”, even though it’s unlikely it’s not impossible.

For a demon who knew the position and velocity of every particle there is no entropy (or it doesn't change if we define one).

Maxwell: “One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving the separate molecules of which they are made up. But if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially as finite as our own, would be able to do what is at present impossible to us.”

You could take a homogeneous gas, use the demon to separate it in hot and cold (using no energy), then use the temperature difference to perform useful work (with any number of engines, such as Sterling's), then use the demon again, and hey presto, you got yourself a perpetual motion machine.

(BTW, one can buy Sterling engines, some of which work with body temperature, ie holding it will create enough temperature difference to turn the engine:



https://en.wikipedia.org/wiki/Stirling_engine )

Thank you whoever chose to downvote. Nothing like punishing genuine curiosity, ay!

It violates entropy because work is being done to the combined system. The subdivided systems, if looked at in their own reference frame, would exchange entropy and mass which is work. After that time, If all else is held equal, your intuition is correct that entropy would be conserved in each subdivided system.

I wonder if Laplace’s demon knows about Maxwell’s.

Laplace’s demon would by definition know if Maxwell’s demon exists or not, wouldn’t it? Whether Maxwell’s demon knows Laplace’s demon is something else entirely.

> Laplace’s demon would by definition know if Maxwell’s demon exists or not, wouldn’t it?

Potentially; however, that depends on how we define knowledge.

Similar to how Maxwell's Demon requires us to take into account information, Laplace's Demon requires us to take into account computation. In particular, we often assume "logical omniscience": that "knowing" something also implies we "know" its consequences; for Laplace's Demon, it "knows" the state of the universe (e.g. positions and velocities of every particle), so we imply that it "knows" all of the consequences (future and past) of that state.

However, logical omniscience implies a solution to the halting problem, which is a logical contradiction. We could avoid this if the Demon were a hypercomputer, but that has its own hyper-halting problems ad infinitum, and is also akin to magic, so less interesting IMHO.

If we instead assume that Laplace's Demon is computable, then the Halting Problem implies it can't "shortcut" its calculations; it has to work through the consequences one step at a time until it reaches the desired state (this is what Wolfram calls "irreducibility"). In other words, the Demon must run an exact simulation of the universe (or at least, the causally-connected part of it).

Personally, I find this quite a nice resolution to the idea of "free will". Our decisions may be completely deterministic, but figuring them out would require a perfect simulation of us; and hence, in a sense, the decision still came from (a perfect copy of) "us".

I think I always figured the “demon” part implies awareness. Otherwise it’s just a simulation, which, as you say, doesn’t necessarily understand anything in the process of doing. Why anthropomorphize something if you’re not going to follow through?

"Awareness" and "understanding", whatever they are, are computable (since the laws of physics are computable, and humans are physical objects). Hence a computable Laplace Demon can certainly have both.

Simulations can also have both (e.g. there's no way to distinguish whether we are a simulation or not).

My point about simulation is that it's the only way for one Turing-complete system to accurately predict the behaviour of another. This is a consequence of the Halting Problem.

For example, let's assume a (computable) Laplace Demon knows the entire state of the particles in a room, which includes a computer that's just started the following command:

    if ./foo.py; then eject /dev/cdrom; fi
Accurately predicting the future motion of those particles must include whether or not the CD-ROM tray comes out. That depends on the exit code of foo.py, exactly when it exits, and indeed on whether it exits (halts) at all!

'Logical omniscience' is the idea that a Demon would instantly "know" all of the future particle behaviour, as soon as it learns the current state; without having to spend time calculating those consequences. Logical omniscience leads to a contradiction, since such a Demon would instantly know if/when foo.py halts for regardless of which program foo.py happens to be. In other words, it would have a computable solution to the Halting Problem, which Turing proved was impossible. Hence computable processes (including Demons, humans, superintelligent AIs, etc.) cannot be logically omniscient.

As I mentioned before, we could get around this by having the Demon be hypercomputational (e.g. with access to a halting oracle); but that's essentially 'magic' and hence not very interesting.

If we stick with the idea of a computable Demon, then it cannot instantly know all future states; it has to calculate them somehow. What possible calculation could a Demon perform, which would accurately predict the state of the room in the example above, for any possible program foo.py? The answer is obvious: it must run the program! The Demon doesn't necessarily need a recognisable Python interpreter; but whatever calculation method it uses to get an accurate prediction, it must be equivalent to a Python interpreter (anything which accurately calculates the behaviour of arbitrary Python programs is, by definition, an implementation of Python).

This is not just some weird edge-case either; lots of physical systems are Turing-complete. For example, the behaviour of gas molecules bouncing around in containers can be used for Turing-complete computation http://lambda-the-ultimate.org/node/4120 (just like we use the behaviour of electrons bouncing around in wires). Likewise the brain is also Turing-complete (if we give it external memory, like pen+paper), since our brains can trace through the steps of Turing-complete languages. Hence any accurate prediction of such systems must involve 'running an interpreter' for the rules of those systems. Or, in other words, running an exact simulation.

The only way for a computable process (even a human mind!) to accurately predict the behaviour of an arbitrary Turing-complete system (whether that's a Python program, gas in a box, a brain, etc.) is to run through every step of an exact simulation, until the desired point.

Hence for Laplace's Demon to accurately predict the behaviour of the Universe, it must exactly simulate the Universe, in its entirety, step-by-step. That's the only way to know what will happen. And in that case, the Demon 'contains' an exact copy of the Universe, which 'from the inside' is indistinguishable from the 'real' Universe (if there even is such a thing).

It's impossible to know whether we are part of Laplace's Demon's calculations.

This article demonstrates that the Newton’s second law involving a system monotonically moving to a higher state of entropy, is wrong.

Maxwell’s demon and it’s experimental incantations show that this is true at multiple scales. For another example, a sheet of graphene and two diodes also acts as an energy pump, although tiny.

Newton’s second law?

This always makes me think someday we’ll be able to store energy with information. Not sure how exactly but I feel like we’ll see that in a few hundred years.

Imagine an sd card holding a few KWH.

Maxwell's Demon reminds me of the argument for intelligent design.

I forget the logic, but someone has shown that life in the primordial ooze does not violate the 2nd law. Can someone link?

The misguided notion that life violates the 2nd law is easily refuted by the observation that a living being is not a closed system, but requires energy (food, sunlight). And putting a living being in an enclosed box does indeed end life fairly soon.

Not sure what the further argument about the primordial ooze is.

If I understand your underlying question, then maybe the topic you are looking for is complexity vs entropy. Where complexity, such as life, would seem to violate the law of entropy.

It may be worth searching "complexity vs entropy", I think I have seen lectures by both Neil deGrasse Tyson and Brian Greene on the topic. I didn't put to much time looking for the lectures, but here is a quick Q/A from Neil's podcast which touches on it https://www.youtube.com/watch?v=uTkpG79cbEE

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