Role of inertia on the performance of Brownian gyrators

Understanding the role of inertia in nanoscale heat transport is fundamental to the design of efficient nano-thermodynamics systems. In this work, we experimentally address the non-equilibrium dynamics of a Brownian gyrator, a paradigmatic model for nano-heat machines, that converts heat flow between two thermal baths into steady-state rotation. Using an optically levitated nanoparticle in a controlled vacuum environment, we study the transition from overdamped to underdamped dynamics of the gyrator. We demonstrate that, while the spatial signature of the non-equilibrium steady state vanishes as damping decreases, the rotational dynamics and energetics are optimized at a critical damping. Our findings reveal the importance of inertia for maximising the performance of nanoscale machines and provide fundamental insights into the design of efficient nano heat engines and processes.