Brownian Ratchet - Why IT Fails

Why It Fails

Although at first sight the Brownian ratchet seems to extract useful work from Brownian motion, Feynman demonstrated that if the entire device is at the same temperature, the ratchet will not rotate continuously in one direction but will move randomly back and forth, and therefore will not produce any useful work. A simple way to visualize how the machine might fail is to remember that the pawl itself will undergo Brownian motion. The pawl therefore will intermittently fail by allowing the ratchet to slip backward or not allowing it to slip forward. Feynman demonstrated that if the temperature of the ratchet and pawl is the same as the temperature of the paddle, then the failure rate must equal the rate at which the ratchet ratchets forward, so that no net motion results over long enough periods or in an ensemble averaged sense. A simple but rigorous proof that no net motion occurs no matter what shape the teeth are was given by Magnasco.

If, on the other hand, is smaller than, the ratchet can indeed move forward, and produce useful work. In this case, though, the energy is extracted from the temperature gradient between the two thermal reservoirs, and some waste heat is exhausted into the lower temperature reservoir by the pawl. In other words, the device functions as a miniature heat engine, in compliance with the second law of thermodynamics. Conversely, if is greater than, the device will rotate in the opposite direction, again functioning as a heat engine.

The Feynman ratchet model led to the similar concept of Brownian motors, nanomachines which can extract useful work not from thermal noise but from chemical potentials and other microscopic nonequilibrium sources, in compliance with the laws of thermodynamics. Diodes are an electrical analog of the ratchet and pawl, and for the same reason cannot produce useful work by rectifying thermal fluctuations in a circuit at uniform temperature.