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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Brownian ratchet | 2/2 | https://en.wikipedia.org/wiki/Brownian_ratchet | reference | science, encyclopedia | 2026-05-05T11:10:52.112794+00:00 | kb-cron |
== History == The ratchet and pawl was first discussed as a second law-violating device by Gabriel Lippmann in 1900. In 1912, Polish physicist Marian Smoluchowski gave the first correct qualitative explanation of why the device fails; thermal motion of the pawl allows the ratchet's teeth to slip backwards. Feynman did the first quantitative analysis of the device in 1962 using the Maxwell–Boltzmann distribution, showing that if the temperature of the paddle T1 was greater than the temperature of the ratchet T2, it would function as a heat engine, but if T1 = T2 there would be no net motion of the paddle. In 1996, J. M. R. Parrondo and Pep Español used a variation of the above device in which no ratchet is present, only two paddles, to show that the axle connecting the paddles and ratchet conducts heat between reservoirs; they argued that although Feynman's conclusion was correct, his analysis was flawed because of his erroneous use of the quasistatic approximation, resulting in incorrect equations for efficiency. Marcelo Osvaldo Magnasco and Gustavo Stolovitzky (1998) extended this analysis to consider the full ratchet device, and showed that the power output of the device is far smaller than the Carnot efficiency claimed by Feynman. A paper in 2000 by Derek Abbott, Bruce R. Davis and Parrondo, reanalyzed the problem and extended it to the case of multiple ratchets, showing a link with Parrondo's paradox.
In 1950, Léon Brillouin discussed an electrical circuit analogue that uses a rectifier (such as a diode) instead of a ratchet. The idea was the diode would rectify the Johnson noise thermal current fluctuations produced by the resistor, generating a direct current which could be used to perform work. In the detailed analysis it was shown that the thermal fluctuations within the diode generate an electromotive force that cancels the voltage from rectified current fluctuations. Therefore, just as with the ratchet, the circuit will produce no useful energy if all the components are at thermal equilibrium (at the same temperature); a DC current will be produced only when the diode is at a lower temperature than the resistor.
== Granular gas == Researchers from the University of Twente, the University of Patras, and the Foundation for Fundamental Research on Matter have constructed a Feynman–Smoluchowski engine which, when not in thermal equilibrium, converts pseudo-Brownian motion into work by means of a granular gas, which is a conglomeration of solid particles vibrated with such vigour that the system assumes a gas-like state. The constructed engine consisted of four vanes which were allowed to rotate freely in a vibrofluidized granular gas. Because the ratchet's gear and pawl mechanism, as described above, permitted the axle to rotate only in one direction, random collisions with the moving beads caused the vane to rotate. This seems to contradict Feynman's hypothesis. However, this system is not in perfect thermal equilibrium: energy is constantly being supplied to maintain the fluid motion of the beads. Vigorous vibrations on top of a shaking device mimic the nature of a molecular gas. Unlike an ideal gas, though, in which tiny particles move constantly, stopping the shaking would simply cause the beads to drop. In the experiment, this necessary out-of-equilibrium environment was thus maintained. Work was not immediately being done, though; the ratchet effect only commenced beyond a critical shaking strength. For very strong shaking, the vanes of the paddle wheel interacted with the gas, forming a convection roll, sustaining their rotation.
== See also == Quantum stirring, ratchets, and pumping Geometric phase § Stochastic pump effect
== Notes ==
== External links ==
The Feynman Lectures on Physics Vol. I Ch. 46: Ratchet and pawl Feynman's Messenger Lectures Coupled Brownian Motors - Can we get work out of unbiased fluctuation? Archived 2009-05-10 at the Wayback Machine Experiment finally proves 100-year-old thought experiment is possible (w/ Video) Articles Astumian RD (1997). "Thermodynamics and kinetics of a Brownian motor". Science. 276 (5314): 917–22. CiteSeerX 10.1.1.329.4222. doi:10.1126/science.276.5314.917. PMID 9139648. Astumian RD, Hänggi P (2002). "Brownian Motors" (PDF). Physics Today. 55 (11): 33–9. Bibcode:2002PhT....55k..33A. doi:10.1063/1.1535005. Hänggi P, Marchesoni F, Nori F (2005). "Brownian Motors" (PDF). Annalen der Physik. 14 (1–3): 51–70. arXiv:cond-mat/0410033. Bibcode:2005AnP...517...51H. doi:10.1002/andp.200410121. S2CID 1724528. Lukasz Machura: Performance of Brownian Motors. University of Augsburg, 2006 (PDF) Peskin CS, Odell GM, Oster GF (July 1993). "Cellular motions and thermal fluctuations: the Brownian ratchet". Biophys. J. 65 (1): 316–24. Bibcode:1993BpJ....65..316P. doi:10.1016/S0006-3495(93)81035-X. PMC 1225726. PMID 8369439. Hänggi P, Marchesoni F (2009). "Artificial Brownian motors: Controlling transport on the nanoscale: Review" (PDF). Reviews of Modern Physics. 81 (1): 387–442. arXiv:0807.1283. Bibcode:2009RvMP...81..387H. CiteSeerX 10.1.1.149.3810. doi:10.1103/RevModPhys.81.387. S2CID 16690300. van Oudensaarden A, Boxer SG (1999). "Brownian Ratchets: Molecular Separations in Lipid Bilayers Supported on Patterned Arrays" (PDF). Science. 285 (5430): 1046–1048. CiteSeerX 10.1.1.497.3836. doi:10.1126/science.285.5430.1046. PMID 10446046. Qiu C, Punke M, Tian Y, Han Y, Wang S, Su Y, Salvalaglio M, Pan X, Srolovitz D J, Han J (2024). Grain boundaries are Brownian ratchets. Science 385 (6712): 980:985. doi:10.1126/science.adp1516