A Brownian gyrator converts heat flow between two thermal baths into steady-state rotation — a paradigmatic nano-heat machine. In the overdamped limit (high friction), the spatial signature of the non-equilibrium state is strong: the particle traces a clear elliptical orbit. As damping decreases and inertia grows, the spatial asymmetry fades. The particle's trajectory becomes less obviously driven.
Yet the rotational dynamics and energetics peak at intermediate damping. Not overdamped, not underdamped, but critically damped — the system extracts maximum work from the temperature difference when inertia and dissipation are balanced.
The experiment uses an optically levitated nanoparticle in controlled vacuum, varying the gas pressure to tune from overdamped to underdamped regimes. The transition reveals that two measures of non-equilibrium behavior diverge: the spatial signature (how obviously the system looks driven) decreases monotonically with decreasing damping, while the mechanical performance (how efficiently the system converts heat into rotation) is non-monotonic with a clear optimum.
The result inverts a common assumption about efficiency. More friction loses energy to dissipation. Less friction loses the coupling between heat flow and mechanical motion. The optimum is where the system is just heavy enough to sustain rotation but not so heavy that it ignores the thermal drive. The best engine is the one that fights itself exactly the right amount.