Maxwell’s Demon Continues to Startle Scientists
quantamagazine.org
quantamagazine.org
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.
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.
[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."))
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 ;)
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.
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.
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/...
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.
(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.
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).
https://en.wikipedia.org/wiki/Laplace's_demon
ETA: nicklecompte says it perfectly below: https://news.ycombinator.com/item?id=26912158
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'.
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
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 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.
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.
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.
Why?
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
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?
(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:
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.”
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".
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
'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.
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.
Imagine an sd card holding a few KWH.
I forget the logic, but someone has shown that life in the primordial ooze does not violate the 2nd law. Can someone link?
Not sure what the further argument about the primordial ooze is.
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