Maxwell's Demon

[u/Expressyoself123]

Hi, I'm currently learning about Maxwell's Demon in stat mech and the whole "where did the entropy go" question. I understand the whole journey to Landauers principle, but I feel like im going crazy over the general proposition in the first place?

Like fundamentally the postulate of being able to open a partition (in any manner) for ZERO energy cost, like we just handwave away the physics of opening the partition and then wonder "OMG where did the free energy go/leave to!?!??"

Like guys... we stated a physically impossible thought experiment, its there, its in the moving of the partition... The partition needs SOME physical prescence to reflect molecules and maintain itself at T of the gas (to allow black body radiation principles to work).

To me its like saying, imagine there was no friction in this water wheel, itll spin forever blah blah blah, then asking "WHY DOES THIS GIVE US FREE ENERGY!?!?"

[u/SnooPets5564]

You can actually handwaved the physics of opening the partition, since you can hypothetically recover the energy when you set it back where it was before.

The waterwheel analogy doesn't work, because you actually can't extract energy if idealized everything.

The real reason it doesn't work is because information is weird. You can ignore the entropy of opening/closing the partition, but you can't ignore the entropy of measuring the particle.

[u/Expressyoself123 → u/SnooPets5564]

But how can you move the partition in the first place without putting work/heat in? Something has to move the partition?? Like there is no way to both have control of the states (PTV) of the chambers if partition is moved quasistatically AND not have some net energy into the system overall? If the partition free to move itself yeah the energy is recovered no net gain, but then theres no way to select how it moves freely, it will just respond to the states of the chambers and allow equilibrium to filter the particles. The act of choosing when to do the opening is what costs energy?

To even be able to measure the temps in both partitions at the same time also requires some knowledge or physical connection between the two chambers, which HAS to allow some form of transfer of thermal energy between them, eg if the demon is in LHS how can it measure the temp or know the velocities of particles in the RHS without somehow forming a connection between the two?

My waterwheel example was a poor example, I was just trying to say we propose all these handwaving conditions then wonder in the end why the physics doesnt match what we observe.

IDK just the whole premise just feels like a bunch of bogus handwaving to create a paradox?

[u/SnooPets5564 → u/Expressyoself123]

You would need to put work in when moving the gate, but you can get the work back out when moving it back. Even saying it does increase entropy to move the partition, the real question is if that entropy is more or less than the amount of entropy lost when sorting the particles by speed. Even if the conductivity and gate movement entropy aren't perfectly zero, they could still be low enough that the entropy would have a net decrease if you used a basic model of thermodynamics.

But yes, the act of choosing when to open is what increases entropy. Landauer's Principle says so. It doesn't matter whether or not the gate is open, because even if it is free to move the gate, the entropy is still increased.

The whole point is that there aren't theoretical limits to some things (such as how little energy to move the gate or how insulated we can make the box). There may be physical limits, but this is being done to test theories, not use. If there is a contradiction in a theoretical idealized case, then either there are theoretical reasons we can't set it up (which is interesting in and of itself) or the theory you are testing is wrong. It isn't about whether or not we can build it, it's whether or not our theories allow something impossible to exist.

[u/Historical-Mix6784 → u/SnooPets5564]

It is impossible to open and close the gate reversibly in finite time such that you could capture a molecule. This is not controversial physics. It is the same reason the power output of the Carnot cycle is zero, it is infinitely slow. 

So your just wrong, there is always an entropy associated with the gate in Maxwell’s demon, handwaving it away is bad physics. 

[u/KamikazeArchon → u/Expressyoself123]

The act of choosing when to do the opening is what costs energy?

According to what law? That is the question. "Choosing costs energy" is not an obvious law of physics, nor is it the conclusion of any law that was known at the time. Indeed, the general belief was that choosing does not cost energy.

As a result of the thought experiment, we have now developed a more complex model for things like entropy and information and how they relate to energy.

Of course it's not a paradox with the benefit of hindsight and a more complete understanding of physics.

[u/OaklandSpiel → u/Expressyoself123]

Here’s a semi practical method to move a partition: imagine a mass oscillating on a spring. No energy is required to catch it at one extreme and hold it there. No energy is required to release it and then catch it at the other extreme.

[u/Historical-Mix6784]

Information is not physical, it is only a way for us to quantify which statistical behaviors are most likely to occur.

Some deeply distraught physicists have come to conclude that knowing more about your system literally causes it's behavior to change. No my dearly misguided friends, interacting with a system causes it to change, not your state of knowledge.

Run a simulation of a gas expanding on a computer (LJ gas, LAMMPS, simple stuff), you can track the microstate of every single particle to numerical precision, you still will see the gas expand. Knowing the microstate didn't suddenly erase entropy or the second law of thermodynamics...

All Maxwell's demon shows is that must be some entropy cost the demon must pay to localize the particles onto the other side of the barrier.

1) Raising and lowering the barrier is impossible to do reversibly if you also want to do it in finite-time (so you can capture a molecule).

2) Another cost is perhaps in the "brain" of the demon, who needs to be able to compute/store/erase information about the states of the particles in order to know when to raise the barrier. Information itself costs no change in entropy, but information processing does, since you need to physically manipulate states in contact with a thermal environment. This is the key connection to Landauers principle.

And in any case the demon is a highly non-equilibrium system, and it is well-known that far-from-equilibrium even the second law of thermodynamics is not exact (https://en.wikipedia.org/wiki/Fluctuation_theorem)

[u/DanRudmin → u/Historical-Mix6784]

Entropy is fundamentally a property of information. It depends on definitions of micro states and macro states and perceived randomness which are not objective physically defined properties.

Entropy and temperature and all the other physical properties of thermodynamics only exist relative to an observer or reference frame with incomplete knowledge.

This is why the laws of thermodynamics are fundamentally different than the other laws of physics and they are the only time-directional laws.

[u/Historical-Mix6784 → u/DanRudmin]

This is completely bogus!  Information and entropy can be defined in a way that is independent of observers. 

[u/Historical-Mix6784 → u/[deleted]]

You only need macrostates for thermodynamics not statistical mechanics. Thermodynamics is only the limit of statistical mechanics for maximum entropy ensembles, where all observers are assumed to be maximally ignorant anyway, so your point is moot. 

And there are many ways to define a statistical temperature beyond thermodynamics. The fluctuation-dissipation theorem is one such way.  

[u/Expressyoself123 → u/Historical-Mix6784]

Yeah, so I think my frustration of this "Demon" is in the whole praising of this a some massive paradox, when like its just not logically set up in the first place?

[u/OaklandSpiel]

Even if the energy to open & close a barrier isn’t completely zero, there’s no way that exertion is going to “exorcise” the demon. The problem is, there’s no lower limit to the energy requirement to open a door. So some design exists that would break the 2nd law.

[u/ababababababacus]

the entropy went into the information processing in the demons brain, opening the door is completely ignorable

[u/johnnybhf]

I feel you. I was at the exact same position. It will get better.

[u/BitcoinsOnDVD]

That's a common criticism.

But let's assume you have some but not much friction by imposing a barrier.

Then I could still build a pump like that:

https://arxiv.org/pdf/0805.4824v2

So we can conclude that we need to include information.

[u/NameLips]

The problem with the Maxwell's Demon thought experiment is the introduction of a magical demon.

If you ever did this experiment in the real world, your device would cost energy. All physical laws would be followed.

So basically if you introduce a magical element of course you will get a nonsensical or paradoxical result. That's like saying "if I had a magical demon that could carry me faster than light, I could break causality" and trying to use it as an argument that special relativity was wrong.

[u/OaklandSpiel → u/NameLips]

But the task is to identify what assumption was the one that caused the apparent paradox. The energy to move the door isn’t it.

[u/Expressyoself123 → u/OaklandSpiel]

This is probably the best phrasing for me to wrap my head around the whole presence of the paradox and learning it.