Is Maxwell's Demon Limited by Energy Required for Door Movement?

[Eric Bretschneider]

Physics students are taught about Maxwell's demon and how by opening and closing a door between two chambers filled with gas. If the demon opens and closes the door to "concentrate" low energy molecules on one side and high energy molecules on the other side he can create a temperature difference from which work can be extracted.

My question is, why is the mass of the door and the energy required to open/close the door ignores? At about room temperature and atmospheric pressure, the collisional rate is going to be on the order of 10 GHz. If the gas is helium (diameter ~62 pm) then the tunnel between the chambers would realistically need to be at least 100 pm wide to allow an atom through.

That implies that the door would have to move at least 100 pm in order to open or close the passage and would have to operate at about 10 GHz. That requires an acceleration/deceleration rate on the order of 8.0E+10 m/sec^2. Given the distance and the mass of the door, the demon needs to expend at least 1.07E-15W to create a temperature difference.

This ignores any energy needed for sensing the speed of an approaching helium atom.

More realistically the tunnel would need to be wider and the door far more massive than a single helium atom. It would also have to withstand accelerations of about 8 billion times that of gravity.

I really question if the energy extracted by results of Maxwell's demon could actually exceed the energy needed to create the temperature difference.

 

[hutchphd]

https://en.wikipedia.org/wiki/Maxwell's_demon

 

[Eric Bretschneider]

https://en.wikipedia.org/wiki/Maxwell's_demon

Those references largely deal with information and entropy. I am asking specifically about the energy needed to open/close the door between compartments.

 

[Nugatory]

My question is, why is the mass of the door and the energy required to open/close the door ignores?

It is a thought experiment, meaning that the objective is to illustrate the theoretical principles that set a limit on the demon's efficiency. The practical issues involving the properties of realistic materials and mechanisms are beside the point - we already understand that the machine can't be built using any currently imaginable technology.

You'll see something similar in explanations of special relativity. Phrases like "a spaceship accelerates to .99c, and ..." are blithely tossed off without any regard for the difficulties involved. It can't be done, but that's irrelevant to the purpose of the discussion.

 

[hutchphd]

Those references largely deal with information and entropy. I am asking specifically about the energy needed to open/close the door between compartments.

You need to choose a door and figure it out. The point of the reference is that even in the best theoretically possible case the demon cannot accomplish the task. If we give hum a heavy door it will be much worse but who cares?

 

[DaveC426913]

If I understand correctly, it's already been shown that Maxwell's Demons can't effectively work against thermodynamics, for a host of reasons.

OP's argument appears to merely add a few more practical reasons why it can't. So, essentially, it's pounding another nail into a coffin that has already been nailed shut.

Or am I misinterpreting the OP?

 

[hutchphd]

I think that is the intent and the OP should by all means attempt the calculation if desired and seek specific help when necessary. He is most certainly correct but it would be useful for him to carry his calculation to the point of providing, say, an estimated lower limit.

 

[Eric Bretschneider]

You need to choose a door and figure it out. The point of the reference is that even in the best theoretically possible case the demon cannot accomplish the task. If we give hum a heavy door it will be much worse but who cares?

I am looking for more specific references on a realistic analysis before finishing the calculations I already started. You will note that I already calculated the minimum energy for operating the door based on helium at STP conditions. If there aren't specific references for a realistic analysis, then I can start writing code to get the answer.

Wikipedia is hardly a definitive source for technical information.

 

[hutchphd]

Good. I find it fascinating that the fundamental limit is the information storage and retrieval requirement.
It is unclear to me how you reached your numerical result. Do you not have to assume some physical parameters for the door (am I missing something?.. did you describe the mass you used?)