The Second Law of Thermodynamics is a beast. As a PhD student I was given from time to time letters from people who claimed that they invented perpetual motion machine (University was obliged to provide answers for letters and obviously all the effort was thrown on poor PhD candidates).
Some of those invention were breaking energy conservation principle - those were easy. But there were some really ingenious ideas how to construct perpetual motion machine that was breaking II Law of Thermodynamics in a rather tricky way. Proving incorrectness was a nightmare sometimes.
From my bag: A friend's husband collared me at an all-weekend outing with some crazy contraption idea of lawnmower engines & generators & other junk. It was a fairly long-winded description followed by a question of "why wouldn't this work?" My reply was simply: Because the gods are out to fuck you over. He just looked into the air and said: I can accept that. The wife (MIT educated): How come when I explain the 2nd law forbids it from working, you keep asking, but when he tells you the gods are out to fuck you over, you accept it?
PS. What university requires answers for such letters?
As an undergraduate in physics I was spared from any absurdity like that, but I knew professors got emails and the like for those types of things. However, the most amusing thing that I heard about was that our department (Physics and Astronomy) would get calls inquiring about their horoscope. Which caused us every year to change our name to Department of Psychics and Astrology on Halloween.
‘ In general, the demon sets some threshold of performance (wins or losses) over a given time period that will tell it whether or not to stop. There’s no unique best gambling strategy, but some are better than others. ’
I believe the device keeps looking at the sensors and checks to see how many times the electron jumped in the "correct" direction, if the device "won" an ammount of times that, according to their historical performance, is above a certain threshold, the proccess is stopped and the device will use the energy it gathered to do work. When all the energy was used, the proccess will be repeated. I have serious doubts about how many real "work" can such a device really do, when you take into consideration the energy necessary to keep the sensors, data keeping, and the "trapdoor" all working. It's like using a tab of how many green candles have appeared before on a stock price chart to decide when to sell, it's a temptative idea, but in the end your results always return to the mean. The 2nd law is an unavoidable beast.
As a probability theorist (who knows very little about physics) I understand this machine as relying on the well-studied and widely debunked martingale fallacy - that you can play until you are slightly ahead, and then stop. Then repeat from the start. Perhaps I am missing something.
If I'm right, there are lots of ways of tweaking this system to make it appear more effective on different time scales and with different constraints. This is exactly what the folklore of 'gambling systems' looks like - although none can violate the laws of probability, they can be optimized to give a better appearance of doing so.
Suppose I told you to go to Vegas, bet $1 on black at roulette. If you lose, bet $1 million on red. If you lose a second time, bet $1 trillion on black. You would probably recognize this as an unworkable strategy quite quickly. Now try another strategy: write the numbers 1, 2, 4, 4, 3, 7 on a piece of paper. Bet the sum of the first amount and the last amount in the list (on an even chance such as red or black). If you win, cross out both numbers. If you lose, write down sum of the two numbers (the amount you lost) at the end of the list. Repeat until all the numbers are crossed out. You're $21 up. Repeat as many times as the number of dollars you want, divided by 21. The second strategy has been highly optimized, not to beat casinos, but to give gamblers the strong sense that they are either guaranteed to win, or that they are coming very close to winning, except for some outlying bad luck.
However, the two strategies are equally constrained by mathematical laws from making you infinitely rich with certainty.
It's amazing that we're at a point where the next step after "I figured out an interesting variation of Maxwell's Demon" is to actually build the demon and try it out.
If I'm understanding this right, this version of Maxwell's Demon has the demon wait for random fluctuations between the chambers, and then close the gate when there's a gradient.
So dumb question then, doesn't this have the same problem with the original, that you have to spend negentropy to measure one side and know if it's higher potential than the other?
Yes, it still falls to the same fate. It just has less intervention so it goes to that fate slower which means you can recover more energy from the system. Is the basic idea.
I'm not sure this adds much to the original thought experiment. Correct me if I'm wrong, but the idea behind Maxwell's Demon was to illustrate the notion of adding information to the system to prevent/slow entropy (information being the decision to swing the trap door one way or the other). This article just seems to describe a physical device that sort of approaches that.
Isn’t this the difference between N=1 and N=1000? If you run an experiment once, you could get lucky and by constraining the timeframe, you prevent the law of averages from catching up to you.
However, try sufficient number of times or for sufficiently long, and you will face gambler’s ruin.
The difference from the gambler's fallacy is that standard gambling systems do not have memory and keep giving the same random results, but the physical system of Maxwell's demon does have an innnate trend towards equilibrium. In the game Maxwell's New Demon is playing, the dice have memory - the more it has won, the less likely it is to win some more, and the more it has lost, the more likely it is to win in the future.
So if the demon wants side A to be hotter than side B but currently there's a random fluctuation that's not in its favor, then unlike a random walk or a gambler in a coin-flip game the long-term expected value is not the current status but the equilibrium with equal temperature on both sides, so if measurements would be free, then this now demon should work. However, they aren't, and apparently the cost of knowing if it's winning (and thus should quit now) or losing (and thus should continue) is larger than the energy value of "the winnnings".
This seems like a good intersection between information & physics. What is the fundamental limit of efficiency in measuring/mutating the state of the system, assuming nearly-ideal transducers and computation?
The resolution of the original "Paradox" of Maxwell's demon is that the demon is unable to perform the measurements required. The fallacy was that the measurements could be "free".
Isn't this the same thing? If you measure your succcess and choose to stop, you expend energy in order to measure whether you have succeeded. If you measure after each particle, you must do lots of measurements for very little gain. If you measure rarely, you can gain a lot of energy but your expected gain is low because the particles will average out?
I've wondered for ages if it might be possible to transfer energy as information.
Consider a hypothetical setup in which two identical (possibly entangled) systems are run. On the sending side the system is observed and additional energy is spent in computation to compute interventions that would have (but did not) result in free energy. These interventions are then sent to the receiving side where the energy spent in computation on the sending side is partially recovered by actually performing those interventions and recovering free energy.
If something like this or at least loosely analogous to it were possible then it would be possible to do something like put up a Dyson swarm in a close solar orbit around the sun and transmit back the energy not as dangerous and difficult to receive microwave beams but as data feeds containing an endless stream of "cheat codes" to obtain apparent (but not really) free energy at the receiving end.
Energy is conserved because a given cheat code can only be used once to intervene where the sender determined an intervention would have worked. More energy must be spent at the sending side than is obtained at the receiving side.
Given that there are environments like close solar orbit where energy is stupidly abundant, it could work very well even if the efficiency of transfer were terrible. Even if you only got say 1% of sent energy, a small-ish Dyson swarm in an orbit between the sun and Mercury could easily power the Earth, a Mars settlement, and a few hundred spacecraft with ion thrusters.
There's an awesome introductory book on information theory which in one chapter resolves Maxwell's demon. The argument is that the energy needed to reliably send a single bit of information (which is needed for making the detector talk to the trap door) depends on the temperature of the fluid (because you have to overcome background noise), and it turns out the minimum energy needed for this communication is exactly equal to the amount that can be recovered from separating out a molecule.
If my understanding is correct (admittedly a big if), it seems the same problem applies to gambling. The energy it takes to communicate whether a gamble has paid off is at least as big as what can be recovered from the gamble.
The book is "An Introduction to Information Theory" by John R Pierce, and it's the most I've ever learned from a $10 paperback.
Nature has no internal mind. Entropy and relativity and space time are as mystical as a bag of potatoes falling on the floor at the grocery store. Thermodynamics, why we study it and why it's important, is as best of a model one can get which strips out the internal mind from nature. No momentum. No charge. Just internal probability and the external environmental constraints needed to maintain it.
What Are Particles?
----------
Not what most people think. Can heat be transferred to or from the object in question? That's one part. Is there a capacity for heat, or a latency between heat transfer and external environment effects? Then you have a particle. So it's not little grains of sand or little specks of dust. Anything that absorbs energy without moving the thermometer or multimeter.
What Is the Second Law?
----------
If there is no conductive surface or convective medium, such as the Sun warming the Earth, what is the medium of heat transfer? Relativity, speeding up and slowing down internal clocks, works just the same for heat transfer. So does uncertainty, nature's built in tolerance of measurement. Their amount is much more than any cloud of dust in the air or specks of pollen in a slide. They have a long time to go before reaching equilibrium. The insight is the Second Law is not some mystical holistic property. It's a bath of internal states working themselves out.
Why Is Explaining This Important?
----------
Entropy, uncertainty, cosmic scales, tend to cower people's ambition. It should send us the other way. Go for coherent control and pair production. Think of applications where the Earth is enveloped in a matter wave, and the medical treatments we could have down to the quantum biological level of mitosis.
Or if we had control of fusion of the Sun. That core is orbiting a black hole. We make it easier for particles to pop in and out of existence on the surface of the black hole, than it is for them to complete an entire orbit. That's a microwave, ready to melt any incoming asteroid, and will likely be humanity's first gravity application, giving a little black hole-ness to our Sun itself!
Part of me thinks humans, at the very high levels of power and state secrets, have been doing this for decades, if not for over a century.
24 comments
[ 5.6 ms ] story [ 67.2 ms ] threadSome of those invention were breaking energy conservation principle - those were easy. But there were some really ingenious ideas how to construct perpetual motion machine that was breaking II Law of Thermodynamics in a rather tricky way. Proving incorrectness was a nightmare sometimes.
Funny times!
Any particularly memorable ones?
From my bag: A friend's husband collared me at an all-weekend outing with some crazy contraption idea of lawnmower engines & generators & other junk. It was a fairly long-winded description followed by a question of "why wouldn't this work?" My reply was simply: Because the gods are out to fuck you over. He just looked into the air and said: I can accept that. The wife (MIT educated): How come when I explain the 2nd law forbids it from working, you keep asking, but when he tells you the gods are out to fuck you over, you accept it?
PS. What university requires answers for such letters?
how did that policy get put into place, that’s fascinating.
Can someone explain this in a simple way?
If I'm right, there are lots of ways of tweaking this system to make it appear more effective on different time scales and with different constraints. This is exactly what the folklore of 'gambling systems' looks like - although none can violate the laws of probability, they can be optimized to give a better appearance of doing so.
Suppose I told you to go to Vegas, bet $1 on black at roulette. If you lose, bet $1 million on red. If you lose a second time, bet $1 trillion on black. You would probably recognize this as an unworkable strategy quite quickly. Now try another strategy: write the numbers 1, 2, 4, 4, 3, 7 on a piece of paper. Bet the sum of the first amount and the last amount in the list (on an even chance such as red or black). If you win, cross out both numbers. If you lose, write down sum of the two numbers (the amount you lost) at the end of the list. Repeat until all the numbers are crossed out. You're $21 up. Repeat as many times as the number of dollars you want, divided by 21. The second strategy has been highly optimized, not to beat casinos, but to give gamblers the strong sense that they are either guaranteed to win, or that they are coming very close to winning, except for some outlying bad luck.
However, the two strategies are equally constrained by mathematical laws from making you infinitely rich with certainty.
So dumb question then, doesn't this have the same problem with the original, that you have to spend negentropy to measure one side and know if it's higher potential than the other?
However, try sufficient number of times or for sufficiently long, and you will face gambler’s ruin.
So if the demon wants side A to be hotter than side B but currently there's a random fluctuation that's not in its favor, then unlike a random walk or a gambler in a coin-flip game the long-term expected value is not the current status but the equilibrium with equal temperature on both sides, so if measurements would be free, then this now demon should work. However, they aren't, and apparently the cost of knowing if it's winning (and thus should quit now) or losing (and thus should continue) is larger than the energy value of "the winnnings".
Isn't this the same thing? If you measure your succcess and choose to stop, you expend energy in order to measure whether you have succeeded. If you measure after each particle, you must do lots of measurements for very little gain. If you measure rarely, you can gain a lot of energy but your expected gain is low because the particles will average out?
Consider a hypothetical setup in which two identical (possibly entangled) systems are run. On the sending side the system is observed and additional energy is spent in computation to compute interventions that would have (but did not) result in free energy. These interventions are then sent to the receiving side where the energy spent in computation on the sending side is partially recovered by actually performing those interventions and recovering free energy.
If something like this or at least loosely analogous to it were possible then it would be possible to do something like put up a Dyson swarm in a close solar orbit around the sun and transmit back the energy not as dangerous and difficult to receive microwave beams but as data feeds containing an endless stream of "cheat codes" to obtain apparent (but not really) free energy at the receiving end.
Energy is conserved because a given cheat code can only be used once to intervene where the sender determined an intervention would have worked. More energy must be spent at the sending side than is obtained at the receiving side.
Given that there are environments like close solar orbit where energy is stupidly abundant, it could work very well even if the efficiency of transfer were terrible. Even if you only got say 1% of sent energy, a small-ish Dyson swarm in an orbit between the sun and Mercury could easily power the Earth, a Mars settlement, and a few hundred spacecraft with ion thrusters.
If my understanding is correct (admittedly a big if), it seems the same problem applies to gambling. The energy it takes to communicate whether a gamble has paid off is at least as big as what can be recovered from the gamble.
The book is "An Introduction to Information Theory" by John R Pierce, and it's the most I've ever learned from a $10 paperback.
Nature has no internal mind. Entropy and relativity and space time are as mystical as a bag of potatoes falling on the floor at the grocery store. Thermodynamics, why we study it and why it's important, is as best of a model one can get which strips out the internal mind from nature. No momentum. No charge. Just internal probability and the external environmental constraints needed to maintain it.
What Are Particles? ----------
Not what most people think. Can heat be transferred to or from the object in question? That's one part. Is there a capacity for heat, or a latency between heat transfer and external environment effects? Then you have a particle. So it's not little grains of sand or little specks of dust. Anything that absorbs energy without moving the thermometer or multimeter.
What Is the Second Law? ----------
If there is no conductive surface or convective medium, such as the Sun warming the Earth, what is the medium of heat transfer? Relativity, speeding up and slowing down internal clocks, works just the same for heat transfer. So does uncertainty, nature's built in tolerance of measurement. Their amount is much more than any cloud of dust in the air or specks of pollen in a slide. They have a long time to go before reaching equilibrium. The insight is the Second Law is not some mystical holistic property. It's a bath of internal states working themselves out.
Why Is Explaining This Important? ----------
Entropy, uncertainty, cosmic scales, tend to cower people's ambition. It should send us the other way. Go for coherent control and pair production. Think of applications where the Earth is enveloped in a matter wave, and the medical treatments we could have down to the quantum biological level of mitosis.
Or if we had control of fusion of the Sun. That core is orbiting a black hole. We make it easier for particles to pop in and out of existence on the surface of the black hole, than it is for them to complete an entire orbit. That's a microwave, ready to melt any incoming asteroid, and will likely be humanity's first gravity application, giving a little black hole-ness to our Sun itself!
Part of me thinks humans, at the very high levels of power and state secrets, have been doing this for decades, if not for over a century.
Horrifying!!!