7 ms·

Maxwell’s Demon Continues to Startle Scientists

88 points by jnord 6y ago

kris-s 6y ago
I wonder if Laplace’s demon knows about Maxwell’s.
- hinkley 6y ago
  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.
  - chriswarbo 6y ago
    > 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".
    - hinkley 6y ago
      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?
      - chriswarbo 6y ago
        "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 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.
c3534l 6y ago
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?"
- FeepingCreature 6y ago
  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_Maxwell._Theory_of_Heat_%281871%29.pdf 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.
  - kryogen1c 6y ago
    >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.
    - TeMPOraL 6y ago
lwhi 6y ago
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?
- lwhi 6y ago
  Thank you whoever chose to downvote. Nothing like punishing genuine curiosity, ay!
  - engineer_22 6y ago
    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.
- FabHK 6y ago
  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://thestirlingengine.com https://thestirlingengine.com https://www.stirlingengine.co.uk/default.asp https://www.stirlingengine.co.uk/default.asp https://en.wikipedia.org/wiki/Stirling_engine https://en.wikipedia.org/wiki/Stirling_engine )
- kgwgk 6y ago
  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.”
PeterWhittaker 6y ago
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.
- PeterWhittaker 6y ago
  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.
  - ttz 6y ago
    Maxwell was - to put it mildly - a pretty bright guy.
- Nomentatus 6y ago
  Evaporation is pretty efficient, as a sorting device. It also doesn't involve computation. But it gets the Demon's job done.
mrfusion 6y ago
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.
engineer_22 6y ago
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?
- FabHK 6y ago
  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.
- throwaway_isms 6y ago
  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 https://www.youtube.com/watch?v=uTkpG79cbEE
FabHK 6y ago
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/DemonsEnginesAndSecondLaw87.pdf 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 https://news.ycombinator.com/item?id=22138224
- ArtWomb 6y ago
  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 ;)
zackees 6y ago
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.
- kgwgk 6y ago
  Newton’s second law?

88 points by jnord 6y ago

kris-s 6y ago

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

hinkley 6y ago
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.
- chriswarbo 6y ago
  > 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".
  - hinkley 6y ago
    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?
    - chriswarbo 6y ago
      "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 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.

c3534l 6y ago

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?"

FeepingCreature 6y ago
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_Maxwell._Theory_of_Heat_%281871%29.pdf 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.
- kryogen1c 6y ago
  >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.
  - TeMPOraL 6y ago

lwhi 6y ago

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?

lwhi 6y ago
Thank you whoever chose to downvote. Nothing like punishing genuine curiosity, ay!
- engineer_22 6y ago
  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.
FabHK 6y ago
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://thestirlingengine.com https://thestirlingengine.com https://www.stirlingengine.co.uk/default.asp https://www.stirlingengine.co.uk/default.asp https://en.wikipedia.org/wiki/Stirling_engine https://en.wikipedia.org/wiki/Stirling_engine )
kgwgk 6y ago
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.”

PeterWhittaker 6y ago

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.

PeterWhittaker 6y ago
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.
- ttz 6y ago
  Maxwell was - to put it mildly - a pretty bright guy.
Nomentatus 6y ago
Evaporation is pretty efficient, as a sorting device. It also doesn't involve computation. But it gets the Demon's job done.

mrfusion 6y ago

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.

engineer_22 6y ago

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?

FabHK 6y ago
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.
throwaway_isms 6y ago
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 https://www.youtube.com/watch?v=uTkpG79cbEE

FabHK 6y ago

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/DemonsEnginesAndSecondLaw87.pdf 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 https://news.ycombinator.com/item?id=22138224

ArtWomb 6y ago
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 ;)

zackees 6y ago

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.

kgwgk 6y ago
Newton’s second law?