Power-Efficiency Trade-off in Finite-Time Quantum Otto Engines

The study of thermodynamic limits in the performance of microscopic heat engines is crucial for understanding thermodynamics at small scales. Similar to macroscopic engines, the power output of a microscopic engine vanishes as it reaches its maximum efficiency, the Carnot bound. Power-efficiency trade-off relations describe this fundamental trade-off between power and efficiency in classical microscopic engines. However, extending these relations to quantum heat engines remains an open question. This presentation addresses the power-efficiency trade-off in quantum heat engines, focusing on the Otto cycle of a quantum harmonic oscillator. Using the quasi-probability representation to map the quantum Otto cycle to a classical analogue, we derive an upper bound on power as a function of efficiency. This bound vanishes as efficiency approaches a quantum mechanical efficiency bound, which is stricter than the Carnot bound. It reflects a tighter constraint on the performance of quantum heat engines. The relation is valid for any finite-time cycle with arbitrary time-dependent driving and the bound is attainable under established conditions. These findings are validated through numerical simulations across various system parameters and cycle protocols.