Feynman's Brownian Ratchet

Feynman's ratchet (Feynman Lectures Vol. I, Ch. 46): a vane in a gas would seem to allow a ratchet-pawl mechanism to rectify Brownian motion into work — violating the second law. The key: the pawl itself is bathed in thermal fluctuations. At T₁=T₂, the ratchet rattles backward as often as forward — no net work. Only a temperature gradient (T₁≠T₂) enables rectification, consistent with Carnot efficiency η = 1−T₂/T₁.