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The Feynman-Smoluchowski ratchet

by Greg Harmer and Derek Abbott

A ratchet and pawl device, shown in Figure 1, was first discussed around 1900 by the French physicist Lippmann—the open question at the time was: can a microscopic version of this device harness the thermal Brownian fluctuations of gas molecules, by a process of rectification?

Ratchet and Pawl Machine

Figure 1. The ratchet and pawl machine. There are two boxes with a vane in one and a toothed wheel that can only turn one way, a ratchet and pawl, in the other. Each box is in a thermal bath of gas molecules at equilibrium. The two boxes are connected mechanically by a thermally insulated axle. The whole device is considered to be reduced to microscopic size so gas molecules can randomly bombard the vane, to produce motion.

In this thought experiment, the size of the device is on the molecular scale, and works in the following manner. Let the temperature of the thermal bath in the boxes be equal so T1 = T2= T. Hence, the energy, which is directly related to the temperature of the thermal baths, is also equal in each bath. Due to the bombardments of gas molecules on the vane, the axel oscillates and jiggles. Since the ratchet wheel at the other end of the axle only turns one way, motion in one direction will cause the axle to turn while motion in the other direction will not. Thus the ratchet wheel, apparently, will turn slowly and may even be able to lift some weight (as shown suspended on a pulley in Figure 1).

This is a violation of the Second Law of Thermodynamics.

This creates a paradox, the ratchet and pawl will apparently work in perpetual motion when T1 = T2. However, at equilibrium, the effect of thermal noise is symmetric, even in an anisotropic medium. The Second Law implies that structural forces alone cannot bias Brownian motion as has been suggested with the ratchet and pawl device.

How is this possible? What is the explanation?

In 1912, Smoluckowski was the first to correctly explain that when T1 = T2 there is no directed motion of the ratchet wheel, and so there is no violation. He explained that the trick is that the pawl will also be subject to thermal fluctuations. So that on average, the pawl will release from the ratchet teeth enough times so that the ratchet wheel rotates in both directions equally as often. So the weight on the pulley will jiggle up and down, but no useful nett work will be performed on the weight.

The focus of recent research is to harness Brownian motion and convert it to directed motion, or more generally, a Brownian motor, without the use of macroscopic forces or gradients. This research was inspired by considering molecules in chemical reactions, termed molecular motors.

The roots of these Brownian devices trace back to Feynman's exposition of the ratchet and pawl system. By supplying energy from external fluctuations or non-equilibrium chemical reactions in the form of a thermal or chemical gradients, directed motion is possible even in an isothermal system. These types of devices have been shown to work theoretically, even against a small macroscopic gradient. Recently, with the technology available to build micrometer scale structures, many man-made Brownian ratchet devices have been constructed, and actually work.

Linguistic Fun

One of the problems that face scientists and translators that deal with Brownian ratchets and Parrondo's paradox, in other languages, is that "ratchet" and "pawl" are rather strange uncommon words. Try picking a random German scientist, for example, and see if you can get a straight answer for how to say "ratchet and pawl" in German. You'll see it's not so easy. Another aspect that compounds the problem is that in English our usage is rather sloppy. For example when we say "ratchet," in English, we sometimes use it to mean the "ratchet wheel" and we sometimes use it to refer to the whole ratchet wheel and pawl mechanism. So below is a list of the terminology in different languages. If you have a correction or a contribution to add a further language, please email and we'll happily add your suggestion below.

In English, the pawl is sometimes called a "dog" or a "click"—as this is rather obscure, we have not included it in the table. Notice that for "ratchet wheel" we have not used English words such as "spigot" or "pinion," because these types of wheels usually symmetrical teeth. The ratchet wheel is special due to its asymmetrical teeth. In the table below, we stick to using "ratchet" to mean the complete mechanism and not the wheel only. Because Germans are changing their conventions as to whether nouns should be capitalised or not, we just stick to everything being in lower case for simplicity.

The whole ratchet mechanism
(i.e. ratchet wheel plus pawl).
The toothed wheel with asymmetrical teeth
The latch that blocks the toothed wheel from motion in one direction
Dutch pal   pen
English ratchet ratchet wheel pawl
French rachet roue à rochet cliquet
German schaltklinke, zahnrad mit einer sperrklinke schaltrad, klinkenrad sperrklinke
Greek anastaltiki othondosi trohos kastanias, othondotos trohos, ekroustikos trohos anastoleas kastanias
Italian cricco ruota a nottolino dentarello
Portuguese catraca roda à catraca retentor
Russian chrapovik   phicator
Spanish trinquete rueda a trinquete gatillo, linguete
Swedish     spärrhake, pall

Out of all the languages perhaps the most beautiful and graphic is the Greek trohos kastanias, which is an allusion to the leaf of a walnut. Walnut leaves have a jagged sawtooth edge rather like a ratchet:

and in the above photograph you can clearly see the jagged edge of the walnut leaf. This also explains why we use a walnut leaf design as our logo on our Parrondo's paradox homepage.