Brownian ratchet

The Brownian ratchet is a thought experiment about an apparent perpetual motion machine postulated by Richard Feynman in a physics lecture at the California Institute of Technology on May 11, 1962 as an illustration of the  laws of thermodynamics. In particular, it is an example of a Maxwell's demon, a machine that is purported to extract useful work from random fluctuations in systems otherwise at equilibrium.

The device consists of an asymmetric gear known as a ratchet that rotates freely in one direction but is prevented from rotating in the opposite direction by a pawl. The ratchet is connected by a massless and frictionless rod to a paddle wheel that is immersed in a bath of molecules at temperature $$T_1$$. The molecules constitute a heat bath in that they undergo random Brownian motion with a mean kinetic energy that is determined by the temperature. Each time a molecule collides with a paddle, it imparts an impulse that exerts a torque on the ratchet. Because the pawl only allows motion in one direction, the net effect of many such random collisions should be for the ratchet to rotate continuously in that direction. The ratchet's motion then can be used to do work on other systems, for example lifting a weight against gravity. The energy necessary to do this work apparently would come from the heat bath, without any heat gradient. Were such a machine to work as advertised, its operation would contradict one form of the second law of thermodynamics, which states that It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.

Although at first sight the Brownian ratchet seems to extract useful work from Brownian motion, Feynman demonstrated that its operation would be self-defeating, and would in fact not produce any work. A simple way to visualize how the machine might fail is to remember that a ratchet and pawl small enough to move in response to individual molecular collisions also would be small enough to undergo Brownian motion as well. The pawl therefore will intermittently fail, allowing the ratchet to slip backward. Feynman demonstrated that if the temperature $$T_2$$ of the ratchet and pawl is the same as the temperature $$T_1$$ of the bath, 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.

If, on the other hand, $$T_2$$ is smaller than $$T_1$$, the ratchet can indeed ratchet forward. In this case, though, energy is extracted from the temperature gradient in agreement with the second law.

Although the Feynman ratchet cannot extract work from a heat bath in equilibrium, this model and related ideas led to the development of Brownian motors, which do extract useful work from thermal noise, but do not violate the laws of thermodynamics.