Rotational Brownian motion (astronomy) supermassive black holes at the centers of galaxies. Perturbations from passing stars can alter the orbital plane of such a binary, which in turn alters the direction of the spin axis of the single black hole that forms when the two coalesce. Rotational Brownian motion is often observed in N-body simulations of galaxies containing binary black holes. The massive binary sinks to the center of the galaxy via dynamical friction where it interacts with passing stars. The same gravitational perturbations that induce a random walk in the orientation of the binary, also cause the binary to shrink, via the gravitational
Perpetual motion costs energy (requiring Maxwell's demon to perform more thermodynamic work to gauge the speed of the molecules than the amount of energy gained by the difference of temperature caused) or the unidirectionality is an illusion and occasional big violations make up for the frequent small non-violations (the Brownian ratchet will be subject to internal Brownian forces and therefore will sometimes turn the wrong way). Buoyancy is another frequently misunderstood phenomenon. Some proposed perpetual-motion machines miss the fact that to push a volume of air down in a fluid takes the same work as to raise a corresponding volume of fluid