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If I had a light "diode" - an object that only allowed light (at least for a range of frequencies) to travel through it in one direction, would this necessarily allow violations of the 2nd Law of Thermodynamics? Or would it be possible to restrict other properties of the device such that it could be okay.

Why I think it should violate 2nd law:

  1. I can place such devices at temperature T in a bath of thermal radiation at temperature T, such that it forms a box which only lets the light in or out. This would appear to always allow one to create a thermal gradient. Once a thermal gradient is formed, useful energy can be extracted. This seems to allow useful energy to always be extracted from a thermal bath and thus give perpetual motion.

  2. Release one such device at temperature T in a bath of thermal radiation at temperature T. Since the photons are absorbed or reflected in one direction, and undisturbed in the other, the device will start moving. It can use a thermal bath to directly generate useful motion.

Why I think I'm missing something and such a device could potentially co-exist with the 2nd Law:

  1. The above arguments seem valid if the diode was only 'partially' rectifying as well. However there exist sunglasses which largely reflect on one side, but not from the other side.

  2. Researchers have succeeded in using meta-materials to create a "blackhole" for microwaves.

Can anyone help sort this out?

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You have to take into account that a diode, like any other piece of equipment, is an inefficient converter of energy into work. More efficient than an incandescent lamp, but it still generates heat. Continued use of the diode in the box in the manner you describe, will cause it to heat up (because we allow only the light emitted by the diode to leave the box) and eventually fail - thereby ceasing to be perpetual. So, no, there are no violations of the 2nd Law in this situation. –  user346 Mar 19 '11 at 18:59
    
The wikipedia article on Maxwell's demon might interest you. en.wikipedia.org/wiki/Maxwell%27s_demon . A number of demonstrations have been made, and entropy always increases or stays the same. –  anna v Mar 19 '11 at 20:30

3 Answers 3

up vote 15 down vote accepted

Light diodes exist, and yet the 2nd law endures. In general, any perfect ratchet would allow you to violate the 2nd law. Since very few Nobel prizes have been awarded for perpetual motion machines, experimental evidence seems to suggest there is no such thing as a perfect ratchet.

When confronted with any type of device that rectifies the flow of energy, the appropriate question, in my opinion, is 'how is this device imperfect'? In the case of a Faraday isolator, Lord Rayleigh addressed this question a long time ago.

EDIT:
The other reference at the end of the Wikipedia article on Faraday isolators is a pretty nice discussion of this topic.

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My understanding is that Faraday isolators are not actually light diodes in the sense defined above: as it would let just as much unpolarized light through in each direction. The only thing that makes them special is that the transmission is polarization dependent in each direction. Otherwise, as noted in the question, a Faraday isolator could act as a propulsion system in a thermal bath such as the cosmic microwave background. –  Edward Mar 20 '11 at 5:21
    
That is not how a Faraday isolator behaves. The Faraday isolator in my old lab gave huge attenuation to back-propagating unpolarized light, in its operation bandwidth. If it didn't, it would have been useless. Look at this image, and imagine what would happen to light going each direction, for each polarization. –  Andrew Mar 20 '11 at 12:52
    
Thanks, you are right. Does this then invalidate (or at least require qualification) the opening paragraph of Lubos' answer? –  Edward Mar 20 '11 at 13:00
    
I think what he wrote is fine, but it's subtle and interesting why. The link I added to my answer discusses this. –  Andrew Mar 20 '11 at 13:15

A light diode that would reflect every photon coming from one side but allowed all photons from the opposite side to be fully transmitted - and that wouldn't absorb anything - would be in contradiction with the second law because that would be nothing else than a photon version of Maxwell's demon: it would be able to collect all particles (photons in this case) in one half of a vessel.

Such things can't exist because the second law demonstrably holds for all objects with many degrees of freedom.

None of the "almost light diodes" from the real world that you mentioned is doing the same thing - mostly because the objects you mention absorb a sufficient fraction of the incoming light from one of the two sides. When they absorb the light, they turn the absorbed photon's energy to heat - a more chaotic form of energy - and increase the total entropy by a sufficient amount so that the overall entropy trend is never negative.

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What about a light diode that only works in a certain range (like the metamaterial microwave blackhole that was built)? Is it possible to have a light diode in one frequency range if the effects in the other frequency ranges somehow 'compensate' for it ... or is there an argument which shows that there can't be rectification in any mode, ie. that detailed balance must hold? –  Edward Mar 20 '11 at 5:16
    
Good question, a new one. I am not sure. It's like the competition between criminals, who try to break the law, and police that tries to fight it. ;-) My guess is that the ban must work even for individual frequencies. –  Luboš Motl Mar 20 '11 at 6:13

The simplest "light diode" (optical isolator) (link) is two polarizing sheets 45 degrees apart, with a 45 degree Faraday rotator in between. The polarizing sheets absorb light with one polarization and transmit it with the opposite polarization.

To check the second law of thermodynamics, you need to assume the polarizing sheets are at the same temperature as the other things you're thinking about. Therefore the polarizing sheets will emit their own blackbody radiation, always polarized in the direction that they absorb light. The device violates the second law of thermodynamics ONLY if you FORGET the blackbody radiation of the polarizing sheets.

Things get more complicated when you replace "polarizing sheets" (which emit blackbody radiation) with "polarizing beamsplitters" (which don't). A polarizing beamsplitter sends each light-polarization in a different direction, for example it might back-reflect one polarization and transmit the other. But no matter where you send the non-transmitted light polarization, you will always end up causing problems for your perpetual motion machine. You can try drawing it out to see the various ways this happens. This paper (linked by Andrew above) goes through some of the possibilities in detail. :-)

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