# Why is it so hard to explain that the Brownian Ratchet doesn't work?

The Brownian Ratchet stood up to a lot of scrutiny before it was finally shown why it would not work as a perpetual motion machine, but it seems weird to me that all of that was necessary. If the particles hitting the paddle caused it to move they would lose energy and slow down. Because of this there is a finite amount of work that the system can do which would make it not a perpetual motion machine. Why is it necessary to show that the pawl undergoes Brownian motion to prove that it won't work?

• Related: physics.stackexchange.com/q/203974 I think the confusion lies in the fact that any entropy-decreaser can be used to make perpetual motion, so we often use the latter term to describe the former. – user10851 Dec 11 '15 at 1:13
• That clears it up a little bit for me, but how does entropy-decreasing lead to perpetual motion? It still wouldn't be able to provide an infinite amount of useful work as far as I understand. – rtpax Dec 11 '15 at 1:42
• To me, it's obvious that a Brownian Ratchet should work, just like it's obvious that cold fusion should work. It's a shame that such nice ideas conflict with reality. – Daniel Griscom Dec 11 '15 at 3:07
• @rtpax perpetual motions of the second kind do not generate energy, they transform more heat into work than otherwise possible, and the heat transformed only becomes infinite if you have an infinite thermal reservoir. en.wikipedia.org/wiki/Perpetual_motion#Classification – user83548 Dec 11 '15 at 14:20

Most proposed perpetual-motion machines are perpetual motion machines of the first kind (that is, they violate the First Law of Thermodynamics, conservation of energy). It's easy to understand why these shouldn't work, and the missing energy source (or the fact that the machine isn't really perpetual) can usually be found quickly.

The Brownian Ratchet is an example of the less-common perpetual motion machine of the second kind. It apparently violates the Second Law of Thermodynamics (entropy in an isolated system cannot decrease), in this case, by generating motion directly from a heat source. Entropy is a much harder concept to understand than energy (it can be thought of as a measure of the "sameness" of the universe), and working out why the Brownian Ratchet doesn't work requires complicated statistical-mechanics calculations.

The key thing to remember when analyzing the Brownian Ratchet is that the Second Law applies to isolated systems as a whole. The paddles aren't isolated from the pawl; a correct analysis needs to take into account the whole paddle/pawl/working fluid system. If you do this, you'll find that, over time, the entropy decrease from molecules hitting the paddles is exactly offset by the entropy increase from molecules hitting the pawl or the pawl's own thermal motion, letting the paddles slip backwards.

Here is another reason why a ratchet should not work: it would define a directional arrow of time even in thermal equilibrium.

To see this look at the modified ratchet in the graph (the triangular piece is attached to a spring). the brownian particle would move easier to the right as it can push the triangular piece down, but if it is at the right and tries to move to the left it will be stopped by the vertical surface (no way to push it down). Our intuition tells us that the particle then will circulate clockwise, even in thermal equilibrium. This defines an arrow of time: you can tell if a movie is shown in reverse. Which cannot be true.

• Are we talking QM here? If so, T is not always symmetric (kaons violate CP, which is the same as T violation). If we're talking classical, then T is certainly not symmetric, or I'll turn my omelette back into an egg. The only real symmetry is CPT. – Oscar Bravo Dec 11 '15 at 15:29
• I am not talking quantum, and your omelette making process is is well away from thermal equilibrium. I believe you agree that, classically, fluctuations in the arrow of time could be in any direction in thermal equilibrium, but a ratchet would violate that. – user83548 Dec 11 '15 at 15:37
• Thermal equilibrium - I forgot about that! +1 :-) – Oscar Bravo Dec 14 '15 at 7:52