The Problem of Detailed Balance for the Feynman-Smoluchowski Engine (FSE) and the Multiple Pawl Paradox

The Feynman-Smoluchowski Engine (FSE) is simply a ratchet and pawl device, connected by a shaft to a vane, that is small enough to rectify the effect of random bombardment of gas molecules on the vane. The significance of the FSE is that it has inspired much activity in the area of Brownian ratchets. There is considerable interest in both the FSE and Brownian ratchets as these models are finding increasing use in a wide range of multidisciplinary applications from stochastic signal processing to econophysics to biology and even sociological processes. In this paper we examine the problem of detailed balance of the FSE and we introduce a new problem that considers a ratchet wheel with multiple pawls.