Molecular Ratchet -- Feynman's explanations

[mischmi]

TL;DR

Molecular Ratchet;

Hi all.
Feynman writes:

When the damping happens, of course, the energy that was in the pawl goes into the wheel and shows up as heat. So, as it turns, the wheel will get hotter and hotter. To make the thing simpler, we can put a gas around the wheel to take up some of the heat. Anyway, let us say the gas keeps rising in temperature, along with the wheel.

https://www.feynmanlectures.caltech.edu/I_46.html
https://en.wikipedia.org/wiki/Brownian_ratchet

1. Does emerging of temperature differences supposedly violate the 2nd law? (yes?)
   As soon as a temperature difference occurs, e.g. a Carnot process could work.
2. or 2nd ratchet in the opposite direction? Energy transfer and temperatures would balance each other out, but the work on the load would remain
3. Are Feynman's explanations of the molecular ratchet still valid?
   I am not convinced by his famous explanations. Is there already any reasonable criticism on his approach out there? Only the case with same temperatures is interesting. Nothing surprising with different temperatures.
   Feynman could/should use or invent a mechanically better working ratchet, different kind of freewheel, or one working continuously. Do Feynman's ratchet and pawl jiggle independently? This is not how ratchet should work.
4. Would just biased movement of a kind of ratchet/freewheel, without load or "useful work" supposedly violate the 2 low? (yes?)
5. Would a (working) molecular ratchet definitely violate the 2nd law of thermodynamics? (no?)
   The ratchet is made up of separate Brownian particles with limited and known mobility, which reduces the entropy of the entire system. (similar to the explanation of Maxwell's demon)
6. Is the 2nd Low Of Thermodynamics the adequate context in studying the kinetic gas theory, spatially molecular ratchet? (no?)
   Kinetic gas theory deals width microscopic, reversible, Newtonian, at particle level (even if "only" statistical) model, and has fluctuations. Thermodynamics don't, is a macroscopic view. Sure, in limit both give equal statements. (Isn't it as you would say "Newton was wrong, because of relativity...", just a question of taking a closer look?)

 

[DrClaude]

Does emerging of temperature differences supposedly violate the 2nd law? (yes?)
As soon as a temperature difference occurs, e.g. a Carnot process could work.

No. The difference in temperature is consistent with normal fluctuations. It would be a very tiny difference in temperature.

Are Feynman's explanations of the molecular ratchet still valid?
I am not convinced by his famous explanations. Is there already any reasonable criticism on his approach out there? Only the case with same temperatures is interesting. Nothing surprising with different temperatures.
Feynman could/should use or invent a mechanically better working ratchet, different kind of freewheel, or one working continuously. Do Feynman's ratchet and pawl jiggle independently? This is not how ratchet should work.

Are Feynman's explanations of the molecular ratchet still valid? Yes. His point was to demonstrate in a simple system how the 2nd law works. There is reason to make things more complicated.

Do Feynman's ratchet and pawl jiggle independently? This is not how ratchet should work.

How can they not move independently?

Would just biased movement of a kind of ratchet/freewheel, without load or "useful work" supposedly violate the 2 low? (yes?)

Moving the ratchet/freewheel can be seen as work done by the gas on the ratchet/freewheel, so that would not be possible.

Would a (working) molecular ratchet definitely violate the 2nd law of thermodynamics? (no?)
The ratchet is made up of separate Brownian particles with limited and known mobility, which reduces the entropy of the entire system. (similar to the explanation of Maxwell's demon)

You can't get around the 2nd law. Molecular ratchet exist, but they rely on differences in temperatures or there is a power source (non-equilibrium conditions).

Is the 2nd Low Of Thermodynamics the adequate context in studying the kinetic gas theory, spatially molecular ratchet? (no?)
Kinetic gas theory deals width microscopic, reversible, Newtonian, at particle level (even if "only" statistical) model, and has fluctuations. Thermodynamics don't, is a macroscopic view. Sure, in limit both give equal statements. (Isn't it as you would say "Newton was wrong, because of relativity...", just a question of taking a closer look?)

The 2nd law is a statistical law, and it can be (temporarily) violated in some small systems. Non-equilibrium thermodynamics is a field on its own.

 

[mischmi]

Thank you very much for your attention, DrClaude.

No. The difference in temperature is consistent with normal fluctuations. It would be a very tiny difference in temperature.

But Feynman argues: "the wheel will get hotter and hotter." " ... turn the axle backwards. And as things get hotter, this happens more often."
Obviously, his idea is, that with every jump of pawl against the gear the potential energy of pawls spring dissipates to heat. It doesn't seem like he means the tiny fluctuations, I mean.

How can they not move independently?

The pawl and gear are partially coupled. The pawl slides on the gear, sometimes the gear helps the pawl to move upwards. The pawl sometimes blocks the gear.
We can imagine a ratchet with a pawl that slides frictionless along the teeth of the gear so it doesn't bounce (which bothers Feynman). The damping is sure there, but it is a property of the Brownian movement and not necessary in pawl-gear collisions as in the thought experiment.

Moving the ratchet/freewheel can be seen as work done by the gas on the ratchet/freewheel, so that would not be possible.

No, it is Brownian movement, it can go from A to B with energy fluctuations only. The energy which accelerates the Brownian particle goes back to gas.

You can't get around the 2nd law. Molecular ratchet exist, but they rely on differences in temperatures or there is a power source (non-equilibrium conditions).

I don't want to get around 2nd law. I am just not convinced by Feynman's example, the first part about same temperatures.
The idea is, that a working (doubt) "better ratchet" doesn't necessarily violate 2nd low. It shouldn't sound crude, but a "Maxwell's deamons brother", sitting on gear, and putting a stick in between teeth of gear at appropriate times, would do the job.

 

[mischmi]

One more

There is reason to make things more complicated.

Nevertheless, I try to simplify.
I think, if we stick with kinetic theory, and if we can control Brownian particles at fluctuations level, we can theoretically earn energy. Help!
Supposed we make a simplified simulation: it will be a system with deterministic, Newtonian behavior, just excited by stochastic forces, in whatever distribution (pressure fluctuations on a nano-paddle).
e.g.

Blue are Brownian forces, green preload force on wedge (like pawl spring), red supposedly movement. Shaded is fixed and thermal isolated, so the friction energy dissipation remains in system (regardless whether we see it kinetic, Newtonian, reversible or thermodynamic, dissipative, irreversible).

If the wedge releases, the bar jiggles statistically in place. If the wedge closes, the bar can only move to the right, if bars and wedges fluctuating forces are greater than preload on wedge (not frictionless!).

Doesn't the bar move biased to the right, and why not?
Please not "no, because 2nd law violation...". A gas kinetic explanation, based on fluctuations, is what I'm looking for.
(maybe the 2nd law just does not apply to this system, just out of context?)

 

[jartsa]

Doesn't the bar move biased to the right, and why not?

Hmm ... the jiggling wedge pushes the bar to the left, the same way as the jiggling bar pushes the wedge to the left, by causing an increase of friction when moving to the left.

 

[mischmi]

Hmm ... the jiggling wedge pushes the bar to the left, the same way as the jiggling bar pushes the wedge to the left, by causing an increase of friction when moving to the left.

Perhaps the gap above the wedge is a bit misleading in the drawing. Green is a spring that closes the gap.
There is no gravity.

The top sketch is supposed to be a linear version of freeweel:

This is possibly more intuitive, but a little difficult to handle mathematically .

 

[mischmi]

The 2nd law is a statistical law, and it can be (temporarily) violated in some small systems. Non-equilibrium thermodynamics is a field on its own.

Well... to grab a Brownian movement at temporary violation would be satisfying :-). (sorry, not polite response, but I can't resist)

• A Brownian particle that is temporarily at high speed (or stopped): is it in equilibrium with the surrounding? Can we discuss it in context of 2nd law, or is it subject to non-equilibrium thermodynamics?
• Isn't "a temporary violation" a shifty formulation?A law, that sometimes applies, sometimes not? Sorry. Maybe physics could/should clearly state "2nd low doesn't apply to small systems".

This is apparently my main issue; a confusing mix of macro- (thermodynamics) and micro- (stat. mech.) model.