Brownian ratchets are devices that rectify microscopic fluctuations, thus producing useful work out of a fluctuating environment. The term “Brownian ratchet” highlights two important elements required for the rectification of fluctuations to take place. First, a fluctuating environment should be present, and indeed the term “Brownian” refers to the archetype of a fluctuating environment: Brownian motion, that is the zig-zag motion of a grain of pollen in a fluid, or more generally the random motion of small particles as the result of the multiple collisions with the molecules surrounding them. The term “ratchet” highlights the second requirement for the rectification of fluctuations: the presence of appropriate asymmetries in the system, so to define a preferential direction of motion. However, there is a third important requirement for the implementation of a Brownian ratchet: the system has to be out of thermal equilibrium. In fact, for systems at equilibrium, the second law of thermodynamics prevents the generation of directed motion out of unbiased fluctuations. This is precisely the topic explored in this chapter.

The basic ideas of a Brownian ratchet goes back to the early twentieth century, when Smoluchowski analyzed a simple mechanical device involving a ratchet and a pawl. This thought experiment, later popularized by Feynman in his book The Feynman Lectures on Physics, Vol. 1 (1962), was introduced to illustrate the limitations imposed by the second law of thermodynamics. As we shall show later, the implications of the second law in this example seem quite counter-intuitive, at first.

The operating principle of the ratchet machine is the same as that of an electrical rectifier, which was studied by Brillouin in 1950. Both are elementary examples of devices that, if they could perform as intended, harvesting thermal fluctuations from their environment to produce work, would be in violation of the second law of thermodynamics.

The second law of thermodynamics

Based on empirical evidence, the second law is a postulate of thermodynamics that limits the occurrence of many processes we know from experience do not happen, even though they are allowed by other laws of physics. For example, the water in a glass at room temperature is never seen to cool itself spontaneously to form ice cubes, releasing energy to its environment. Such transformation satisfies the law of conservation of energy, yet it is common sense it never occurs.