Brownian ratchet

The Brownian ratchet is a thought experiment about an apparent perpetual motion machine conceived by Richard Feynmancite book
last = Feynman
first = Richard P.
authorlink =
coauthors =
title = The Feynman Lectures on Physics, Vol. 1
publisher = Addison-Wesley
date = 1963
location = Massachusetts, USA
pages = Chapter 46
url =
doi =
id =
isbn =0201021161 ] in a physics lecture at the California Institute of Technology on May 11, 1962 as an illustration of the laws of thermodynamics. The simple machine, consisting of a paddlewheel and a ratchet, appears to be an example of a Maxwell's demon, able to extract useful work from random fluctuations in a system at thermal equilibrium. Feynman's detailed analysis showed why it cannot actually do this.

The machine

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 (the mechanism is imagined to be small enough that this tiny force could move it). 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.

Why it doesn't 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.

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.

See also

* Brownian motor
* Quantum stirring, ratchets, and pumping

Footnotes

External links

* [http://monet.physik.unibas.ch/~elmer/bm/#why Why is a Brownian motor not a "perpetuum mobile" of the second kind?]
* [http://www.kawai.phy.uab.edu/research/motor/ Coupled Brownian Motors - Can we get work out of unbiased fluctuation?] ;Articles
* R. D. Astumian (1997). [http://www.sciencemag.org/cgi/content/abstract/276/5314/917 "Thermodynamics and kinetics of a Brownian motor"] , Science 276, p. 917-922.
* R. D. Astumian and P. Hänggi (2002) " Brownian Motors ". [http://www.physik.uni-augsburg.de/theo1/hanggi/Papers/309.pdf] , Physics Today 55 (11) , p. 33 - 39.
* P. Hänggi , F. Marchesoni and F. Nori (2005) " Brownian Motors ". [http://www.physik.uni-augsburg.de/theo1/hanggi/History/BrownianmotorsAnnPhys.pdf] , A.. Physik (Leipzig) 14, p. 51 - 70.
*Lukasz Machura: "Performance of Brownian Motors". University of Augsburg, 2006 ( [http://www.opus-bayern.de/uni-augsburg/volltexte/2006/222/ PDF] )
* C. S. Peskin, G. M. Odell, and G. F. Oster (1993). [http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=8369439 "Cellular Motions and Thermal Fluctuations: The Brownian Ratchet"] , Biophysical Journal 65 p. 316-324
* Peter Hanggi, Fabio Marchesoni, "Artificial Brownian motors: Controlling transport on the nanoscale". Review: arXiv:0807.1283 [http://arxiv.org/abs/0807.1283]