We consider the quality factor Q, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, both in classical and quantum mechanics, sets the bound Q=3/8 when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable and momentum-conserving systems can achieve the value Q=1/2, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.
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