Brownian ratchet a heat bath in that they undergo random Brownian motion with a mean kinetic energy that is determined by the temperature. The device is imagined as being small enough that the impulse from a single molecular collision can turn the paddle. Although such collisions would tend to turn the rod in either direction with equal probability, the pawl allows the ratchet to rotate in one direction only. The net effect of many such random collisions would seem to be that the ratchet rotates continuously in that direction. The ratchet's motion then can be used to do work on other systems,
Brownian motion which differs from Smoluchowski by 27/64 can only be put in doubt." Smoluchowski attempts to answer the question of why a Brownian particle should be displaced by bombardments of smaller particles when the probabilities for striking it in the forward and rear directions are equal. If the probability of "m" gains and "n" − "m" losses follows a binomial distribution, with equal "a priori" probabilities of 1/2, the mean total gain is If "n" is large enough so that Stirling's approximation can be used in the form then the expected total gain will be showing that it increases as the