Inertia Tames Fluctuations in Autonomous Stationary Heat Engines

Abstract: Thermodynamic uncertainty relations (TURs) provide fundamental constraints on the interplay between power fluctuations, entropy production, and efficiency in overdamped stationary autonomous heat engines. However, their validity in underdamped regimes remains limited and less explored. Here, we analytically and numerically study a physically realizable autonomous heat engine composed of two underdamped continuous degrees of freedom coupled to a two-level system. We show that this nonlinear setup can robustly violate TUR-based trade-offs by exploiting resonant coupling, effectively using one underdamped mode as an internal periodic drive. When this coupling is suppressed, the system recovers TUR-like bounds consistent with overdamped theory. Importantly, we demonstrate that the strongest suppression of current fluctuations occurs in a resonance regime that can be directly inferred from mean current measurements - a quantity typically much easier to access experimentally than fluctuations. Our results reveal new pathways to circumvent classical TUR constraints in underdamped systems and provide practical guidelines for designing efficient, precise microscopic engines and autonomous clocks.