Maxwell's Demon Paradox: Solving the Puzzle Without Memory Requirements

[Deepblu]

The resolution for Maxwell's demon paradox is that the demon has limited memory and the demon will eventually run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system.

My question is we can do the same thought experiment without the requirement for any memory, here for example:

Instead of high & low energy particles + door, we can put high & low frequency waves in the box and then separate them with a separator that has high pass filter in one direction (located in the upper part of the separator), and a low pass filter in the opposite direction (located in the lower part of the separator). This way overtime low frequency waves will move to one box, and high frequency waves will move to the other box. And because the high frequency waves carry higher energy, we will end up with one box having higher energy content that the other one. No memory is needed here.

What I am missing?

 

[Dale]

a separator that has high pass filter in one direction (located in the upper part of the separator), and a low pass filter in the opposite direction (located in the lower part of the separator).

No such filters exist.

 

[Deepblu]

No such filters exist.

One-way waveguides exist:
https://ieeexplore.ieee.org/document/4382385/

 

[Dale]

One-way waveguides exist:
https://ieeexplore.ieee.org/document/4382385/

The article is behind a paywall, so all I can see is the title and abstract. However, from that it does not appear to be the waveguide alone that permits this, but rather the combination of the waveguide and the cavity. So you may not be able to preferentially move a different frequency the other direction.

 

[anorlunda]

What I am missing?

So, you have an idea to violate the 2nd law of thermodynamics. You invest one minute to write a post, and then expect experts to analyze it and tell you what you're missing? That is very inconsiderate and a borderline violation of PF rules.

The obligation is on you to think your idea through and to do some analysis, and perhaps experiments and write it up in a paper to submit for peer review.

 

[Deepblu]

So, you have an idea to violate the 2nd law of thermodynamics. You invest one minute to write a post, and then expect experts to analyze it and tell you what you're missing? That is very inconsiderate and a borderline violation of PF rules.

The obligation is on you to think your idea through and to do some analysis, and perhaps experiments and write it up in a paper to submit for peer review.

No.. I am just here to learn.

 

[Deepblu]

The article is behind a paywall, so all I can see is the title and abstract. However, from that it does not appear to be the waveguide alone that permits this, but rather the combination of the waveguide and the cavity. So you may not be able to preferentially move a different frequency the other direction.

I am not sure what is your point.
In the example I gave, we have 2 separate waveguides that filter waves in opposite directions.

 

[Demystifier]

One-way waveguides exist:
https://ieeexplore.ieee.org/document/4382385/

First, they say that "One-way electromagnetic waveguide modes are theoretically demonstrated" (my bolding), not that such a waveguide actually exists in the laboratory.

Second, it's possible that they made some error in their theoretical analysis (it's hard to tell without seeing the whole paper).

Third, and most important, the existence of such a waveguide is not automatically a violation of the second law. For instance, a fridge is doing something similar, in the sense that it achieves that the interior contains only "slow" low temperature molecules, while the exterior contains only "fast" high temperature molecules. Nevertheless, the total entropy of the fridge and its exterior increases, so fridge is not a Maxwell demon. Likewise, if the one-way guide works at all, it works such that the total entropy (entropy of the waves + entropy of the wave guide + entropy of their environment) increases.

So what you are missing is the entropy of the wave guide itself and its environment.

 

[Demystifier]

The resolution for Maxwell's demon paradox is that the demon has limited memory and the demon will eventually run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system.

My question is we can do the same thought experiment without the requirement for any memory, here for example:

Instead of high & low energy particles + door, we can put high & low frequency waves in the box and then separate them with a separator that has high pass filter in one direction (located in the upper part of the separator), and a low pass filter in the opposite direction (located in the lower part of the separator). This way overtime low frequency waves will move to one box, and high frequency waves will move to the other box. And because the high frequency waves carry higher energy, we will end up with one box having higher energy content that the other one. No memory is needed here.

What I am missing?

Suppose first that the filter is not autonomous, i.e. that you are the operator working on the filter. Each time you send a high or low frequency wave in one or another direction, you either (i) remember what you have done of (ii) forget it immediately after doing it. In the case (i) you eventually run out of your brain storage space, so eventually you must forget it which increases the entropy. In the case (ii) you increase entropy each time when you forget what you have just done. In each case, you increase entropy one way or another.

Now suppose that the filter is autonomous. Is the autonomous filter any different? No. Your brain is based on the same laws of physics as is the autonomous filter. So even without the brain, there are still some physical degrees of freedom in the filter that keep track of what happened with them during the interaction with waves. Either these degrees of freedom keep track of it permanently [which corresponds to the case (i)] or they don't [which corresponds to the case (ii)].

So what you are missing is that in the autonomous filter there is still some kind of "hidden" memory involved. If the filter interacts with the wave such that the wave suffers a change, then the filter must also suffer a change (this is related to the Newton's third law). That change in the filter is a kind of memory.

 

[Dale]

I am not sure what is your point.
In the example I gave, we have 2 separate waveguides that filter waves in opposite directions.

I don’t think that is possible. The abstract of the article certainly doesn’t make that claim.

In particular, it mentions a waveguide connecting two different cavities, and it mentions that the cavity interacts with the waveguide to produce the one way effect. So there is no indication that the effect can be reversed and some reason to believe that it cannot.

And as others have mentioned, the mere existence of such waveguides does not directly imply anything about the entropy.

 

[Cthugha]

I am not sure what is your point.
In the example I gave, we have 2 separate waveguides that filter waves in opposite directions.

All of the "filters" that operate this way are basically variants of optical Faraday isolators. Consider for example a Faraday isolator or a topological insulator, where the degeneracy between the forward and the backward edge state is lifted or even something as simple as a twisted resonator setup coupled to an ensemble of Rydberg atoms (nice example: Phys. Rev. A 97, 013802 (2018), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.013802).

All of these designs have something in common: In order to create this kind of directional asymmetry, you need a system, where time-reversal symmetry is already explicitly broken locally. Most of the time, this is a consequence of a magnetic like in Faraday rotators. However, all of these kinds of symmetry breaking rely on considering the magnetic field as an external perturbation (If you included the magnet and reversed also the electron flow inside them, full time-reversal symmetry would hold again). Accordingly, employing such filters automatically means that you investigate a system that is not really a closed system and you need to consider the external part as well to get a complete picture about the entropy of the system.

For Fermions, you directly see from Kramer's theorem that every eigenstate of the system with time-reversal symmetry is twofold degenerate and therefore the filter you propose cannot be constructed for a system with time-reversal symmetry. For bosons this is a bit more complicated.

 

[Deepblu]

All of the "filters" that operate this way are basically variants of optical Faraday isolators. Consider for example a Faraday isolator or a topological insulator, where the degeneracy between the forward and the backward edge state is lifted or even something as simple as a twisted resonator setup coupled to an ensemble of Rydberg atoms (nice example: Phys. Rev. A 97, 013802 (2018), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.013802).

All of these designs have something in common: In order to create this kind of directional asymmetry, you need a system, where time-reversal symmetry is already explicitly broken locally. Most of the time, this is a consequence of a magnetic like in Faraday rotators. However, all of these kinds of symmetry breaking rely on considering the magnetic field as an external perturbation (If you included the magnet and reversed also the electron flow inside them, full time-reversal symmetry would hold again). Accordingly, employing such filters automatically means that you investigate a system that is not really a closed system and you need to consider the external part as well to get a complete picture about the entropy of the system.

For Fermions, you directly see from Kramer's theorem that every eigenstate of the system with time-reversal symmetry is twofold degenerate and therefore the filter you propose cannot be constructed for a system with time-reversal symmetry. For bosons this is a bit more complicated.

+1

You are right, I was going to comment on time asymmetry after I found this articles:
One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal
https://web.stanford.edu/group/fan/publication/Yu_PRL_100_023902_2008.pdf

Particularly this quote from the article above: "Breaking time-reversal symmetry lifts the degeneracy at the Dirac point and creates a band gap. An edge state introduced into this gap then behaves as a one-way waveguide."

Also I found this:
https://archive.siam.org/meetings/nw10/soljacic.pdf

As I understood these theorized one way wave-guides, can only work in a system where time symmetry is broken, and thus they do not violate 2nd low of thermodynamics.

 

[Demystifier]

As I understood these theorized one way wave-guides, can only work in a system where time symmetry is broken

There is a simple heuristic way to understand that generally. If something can move in one direction but not in the opposite one, that means that it can have the velocity
$$v=\frac{dx}{dt}$$
but not the opposite velocity
$$v'=-v=-\frac{dx}{dt}$$
The opposite velocity can be written as
$$v'=\frac{dx}{d(-t)}$$
so, loosely speaking, the inability the have the opposite velocity is the same as the inability to describe the system with the inverted time.

 

[sophiecentaur]

One-way waveguides exist:
https://ieeexplore.ieee.org/document/4382385/

Is this any different from a (common) waveguide isolator (or circulator), based on ferrite. (http://www.m2global.com/products/?gclid=CjwKCAjwhevaBRApEiwA7aT533N0BKGzdm3gY3ok2QlgKIwiBkdqtwrejFEbHWZ0DYXucond_k-xHxoCbz8QAvD_BwE) An isolator prevents a reflected wave getting back down the wave-guide (or co-ax) by absorbing it. That would not be what's needed here, I think.