## Saturday, December 13, 2014

### The remote Maxwell Demon

During the summer, I wrote a paper that I dumped in an arxiv category called cond-mat.stat-mech, and then managed to entirely forget about it. So somewhat belatedly, here is a summary.

Pretty much the only recollection I have of my stat mech lectures is that every single one of them was inevitably accompanied by the always same divided box with two sides labeled A and B. Let me draw this for you:

Maxwell’s demon in its original version sits in this box. The demon’s story is a thought experiment meant to highlight the following paradox with the 2nd law of thermodynamics.

Imagine the above box is filled with a gas, and the gas is at a low temperature on side A and at a higher temperature on side B. The second law of thermodynamics says that if you open a window in the dividing wall, the temperatures will come to an average equilibrium value, and in this process entropy is maximized. Temperature is basically average kinetic energy, so the average speed of the gas atoms approaches the same value everywhere, just because this is the most likely thing to happen

The system can only do work on the way to equilibrium, but no longer once it’s arrived there. Once you’ve reached this state of maximum entropy, nothing happens any more, except for fluctuations. Unless you have a Maxwell demon...

Maxwell’s demon sits at the dividing wall between A and B when both sides are at the same temperature. He opens the window every time a fast atom comes from the left or a slow atom comes from the right, otherwise he keeps it closed. This has the effect of sorting fast and slow atoms so that, after some while, more fast atoms are on the right side than on the left side. This means the temperatures are not in equilibrium anymore and entropy has decreased. The demon thus has violated the second law of thermodynamics!

Well, of course he hasn’t, but it took a century for physicists to pin down the exact reason why. In brief it’s that the demon must be able to obtain, store, and use information. And he can only do that if he either starts at a low entropy that then increases, or brings along an infinite reservoir of low entropy. The total entropy never decreases, and the second law is well and fine.

It has only been during recent years that some versions of Maxwell’s demon have been experimentally realized in the laboratory. These demons use essentially information to drive a system out of equilibrium, which can then, in principle, do work.

It occurred to me that this must mean it should be possible to replace transfer of energy from a sender to a receiver by transfer of information, and this information transfer could take place with a much smaller energy than what the receiver gets out of the information. In essence this would mean one can down-convert energy during transmission.

The reason this is possible is that the relevant energy here is not the total energy – a system in thermal equilibrium has lots of energy. The relevant energy that we want at the receiving end is free energy – energy that can be used to do work. The signal does not need to contain the energy itself, it only needs to contain the information that allows one to drive the system out of equilibrium.

In my paper, I have constructed a concrete example for how this could work. The full process must include remote measuring, extraction of information from the measurement, sending of the signal, and finally making use of the signal to actually extract energy. The devil, or in this case the demon, is in the details. It took me some while to come up with a system simple enough so one could in the end compute the energy conversion and also show that the whole thing, remote demon included, obeys the Carnot limit on the efficiency of heat engines.

In the classical example of Maxwell’s demon, the necessary information is the velocity of the particles approaching the dividing wall, but I chose a simpler system with discrete energy levels, just because the probability distributions are then better to deal with. The energy extraction that my demon works with is a variant of stimulated emission that is also used in lasers.

The atoms in a laser are being “pumped” into an out-of equilibrium state, which has the property that as you inject light (ie, energy) with the right frequency, you get out more light of the same frequency than you sent in. This does not work if the system is in equilibrium though, it is then always more likely that the injected signal is absorbed rather than that it stimulates a net emission.

However, a system in equilibrium always has fluctuations. The atoms have some probability to be in an excited state, a state in which they could be stimulated to emit light. If you just knew which atoms were in the excited state, then you could target them specifically, and end up with twice the energy that you sent in.

So that’s what my remote demon does: It measures out of equilibrium fluctuations in some atomic system and targets these to extract energy. The main point is that the energy sent to the system can be much smaller than the extracted energy. It is, in essence, a wireless battery recharger. Except that the energies in question are, in my example, so tiny that it’s practically entirely useless.

I’ve never worked on anything in statistical mechanics before. Apparently I don’t even have a blog label to tag it! This was a fun project and I learned a lot. I even made a drawing to accompany it.

1. Atoms are so...complicated. Using naked electrons, the system unruns itself:

A hermetically isolated hard vacuum envelope contains two closely spaced but not touching, in-register and parallel, electrically conductive plates having micro-spiked inner surfaces. They are connected with a wire, perhaps containing a dissipative load (small motor). One plate has a large vacuum work function material inner surface (e.g., osmium at 5.93 eV). The other plate has a small vacuum work function material inner surface (e.g., n-doped diamond "carbon nitride" at 0.1 eV). Above 0 kelvin, spontaneous cold cathode emission runs the closed isolated system. Emitted electrons continuously fall down the 5.8 volt potential gradient. Electron evaporation from carbon nitride cools that plate. Accelerated collision onto osmium warms that plate. Round and round. The plates never come into thermal equilibrium when electrically shorted. The motor runs forever.

As with quantum gravitation, SUSY, and dark matter, the math is rigorous but a founding postulate is demonstrably incomplete. It is necessary but not sufficient to say "Second Law violation." Find the error. Hint: Je v druhé větě před jeho čárkou.

2. Why was this a paradox for so long? The answer is obvious. The demon has to open the window very quickly for the fast moving particles. That requires more energy, force, and sweat and heat generated by the demon. Hence more entropy. Probably enough to compensate.

3. @Vince V:

1) Particles have (de Broglie) wavelengths; larger momentum, smaller wavelength. The Demon is an optical cutoff reflection or anti-reflection coating. Use photons or neutrons.

2) A spintronic diode passes spin-down electrons in only one direction. An equilibrium spin mixture spontaneously disequilibrates. Given a uniform magnetic field, compartment temperatures spontaneously diverge.

3) A low pressure cryogenic molecular beam of diatomic hydrogen gas is microwave partially pumped into hydrogen atoms, protons, and electrons. The electrons are, before collisions, at a much higher temperature (smaller masses more easily follow EM field oscillations) than the heavier particles. Send the charge-neutral mixed beam over an electrically insulated charged plate. Hot electrons spontaneously unmix from warm protons, cool atoms, and cold molecules.

Find the errors.

4. A difference in thermodynamic symmertry as relations of information is not a paradox of the second law. It is how we incorporate the third law into physicality which would require it to be ultimately a necessary law, a sort of paradox solved by superdeterminism. But there may be n further laws. There is Maxwell's currents to consider as residual.
But if that is experimentally verified where chirality is descriptive, divices that reversed such symmetry would be useful as a sort of lens to determine background polarization and differences as chirality. Uncle AI. Good post. Current passing thru a Germanium crystal log shaped over flat slices heats the wide end and cools the narrow end. But so do vortexes of air in a Hirsch tube.

5. Hello Bee,

“These demons use essentially information to drive a system out of equilibrium…”

Would you have handy a link to one of these experimental treatments of Maxwell’s demon in which information is used in this fashion?

Thanks.

6. I found the references in your paper, thanks.

7. Negentropic phenomena are quite common and the magnetic motors may work with this principle.

8. The concept of remote measurement may contain caveats for its utilization with remote Maxwell demon, which depend on finite life-time of metastable state. Until the information is not transferred fast enough, it will be destroyed and thermalized - it just means, that the demon cannot be very remote. The noisy environment will also lead into destruction of information along its path. This doesn't mean, that we cannot drain the energy from metastable state - it just means, that the above derivation may not be physically sensible.

Also, I'm always suspicious to formal approaches which work with abstract information instead of physically measurable energy. How the fully programmed memory differs from this randomly arranged one? The information content of the first memory is very high, whereas its energy content is equal to the later one.

9. Vince: Saying it's obvious doesn't make it obvious. Try to prove that opening the window leads to a net entropy increase. The energy necessary to move the window could be arbitrarily small. Best,

B.

10. Don,

Yes, sorry, I meant to add the links, as you've meanwhile seen its reference 9 and 10 in my paper:

http://www.nature.com/nphys/journal/v6/n12/full/nphys1821.html

http://www.nature.com/nature/journal/v445/n7127/full/nature05452.html

Best,

B.

11. Sabine,
I find this one of your more challenging posts.

12. Bee,
I cannot make out this sentence in your paper:

“There is, in principle, no reason why the demon has to do its work the system that eventually generates work from the demon’s information, hereafter referred to as ‘the
machine’.”

Thanks.

13. Don,

Thanks for catching this - there's a part of this sentence missing, it should be something like:

"“There is, in principle, no reason why the demon has to do its work DIRECTLY IN CONTACT WITH the system that eventually generates work from the demon’s information, hereafter referred to as ‘the
machine’.”

Strange that, must have accidentally cropped this. Best,

Sabine

14. Bee,

While you manage to avoid the expression, the title of one of your referenced papers bills itself as a “demonstration of information-to-energy conversion.” I understand the sense in which this is said, but I hope you will agree that this statement is at best imprecise.

Surely the information in question would be acting more as catalyst through precise tuning of the signal and is not itself metabolized into energy.

Thanks

15. Don,

Yes, I agree with you, it's not a good way to put it. Best,

B.

16. Don,

"Before we can make an apple pie we first need a universe."

Is the universe itself a catalyst? How far should we fine tune the words?

If there can be entropy involved with information and heat or time, why not energy itself metabolized? Signals as the information itself taking time reaching a remote place that distance can make time stop as well distance vanishing? Lots of words to fine tune here. At least two conceptual methods and two distinct types of information to describe useful differences between them. Where does the magnetism go if there is no electric field in motion ultimately? I do not understand this simple concept in words.

But on such abstract horizons it certainly feels we can eat the information and energy is at best a catalyst. The little demon inside my skull is up to something but I cannot say what.

17. This comment has been removed by the author.

18. There's a running cottage industry built around:
1) Find some dissipative dynamics which allows a fixed point with some coherences
2) Show that these allow the resulting quantum heat engine to enjoy some funny efficiency.

http://www.prl.res.in/~library/Agarwal_GS_2003_3abst.pdf

http://www.pnas.org/content/108/37/15097.full.pdf

It's a cool game - but it usually tends to involve beating detailed balance through some fine tuning within some parameter space of generators of quantum dynamical semigroups.

A good physicist would ask what kind of symmetries are required of the correlation functions to accomplish the fine tuning. Unfortunately, many who like to play this game approach it as an unstructured optimization problem- you will see the phrase "genetic algorithm" in their papers, which means you'll never know where they buried the bodies of their former students.:)

19. zeGoggles...

It rains on the just and the unjust.
Small individual turf holders cannot stand up against bigger land owner operations.
If we control the rain in the desert or the jungle wetlands if a puddle forms that may connect to the swamp an individual aspiring student owns less and less other than the right to be pol bearers of once influential faculty who caved in to the growing bureaucy of administration.
I disagree with your criteria. Asymmetry is equally important and we begin to see cutbacks for the universities. 80% goes to admistrations. 50% for hard research. In USA. But cuts affect that more. But the rain and watershed are already contaminated so economics and cut backs promoting more ignorance will have little to change that. We cannot progress with wisdom without thermodynamic symmetry with it fixed points not programed in the ill understood genetic algorithms in our current states of contaminated minds.

20. "Work Measurement as a Generalized Quantum Measurement"
http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.113.250601
Phys. Rev. Lett. 113, 250601 (2014)
DOI: 10.1103/PhysRevLett.113.250601
related, arXiv:1409.3812

Maxwell's demon, quantitiated.

21. Uncle AI,
interesting speculation that assumes there can be such an algorithm if there can be one for quantum computation in the first place.
Which is quantized, the demon or the spacetime.? The generalization may not resemble either classical or quantum logic. What is continuous or discrete may be one quasi concept. They way out is closer to find physical path solutions more along Sabines modeling. Is there one monopole containing a multiverse or in one universe many monopoles?
Whatever the case we do need to solve the problem of dissipating heat buildup in supercomputer circuits.
It is not clear we can define open or closed container systems nor if natural condensing or crystallization of physicality concepts cannot have a simple description of molecules and atoms complexity. As effective analog experiments suggest. Your first comment post mentions plates and evaporation but there are equivalent models to qualitatively describe that.

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