Feynman's Brownian Ratchet

Feynman's insight (1963): The ratchet-and-pawl seems to convert thermal fluctuations into directed work — the vane would spin preferentially forward. But the pawl itself fluctuates! When T₁ = T₂ = T, the probability of the pawl thermally lifting equals the probability of the tooth ratcheting back, exactly canceling the asymmetry. No net work is extracted — the Second Law holds. Only when T₁ ≠ T₂ does the machine work, with Carnot efficiency η = 1 − T₂/T₁. This is the basis of molecular motors: they work because they are driven by ATP, not thermal noise alone.