Role of System-Bath Interaction in Non-Markovian Quantum Brownian Otto Cycles

Abstract: We study finite-time quantum Otto cycles whose working medium is a harmonic oscillator undergoing a quantum Brownian motion described by the Caldeira-Leggett model when the oscillator is in contact with heat baths in isochoric processes. The time evolution of the Otto cycle is studied by analytically solving the exact Heisenberg-Langevin equations for the system variables and the interaction energy between the system and the bath. This enables us to investigate non-Markovian strong-coupling effects on the quantum Otto cycle. We obtain cyclic steady states and study the thermodynamic properties of the Otto cycle for various values of the parameters describing the heat baths and the coupling between the system and the bath. We compare our results with those obtained in the Markovian limit, where the time evolution is described by the Lindblad equation. We find that the change in the interaction energy during the isochoric process contributes to both work and heat, and plays a crucial role in determining thermodynamic behavior of the cycle. In particular, we find that when the Otto cycle operates as an engine, the effect of the interaction energy is to reduce the work output. We also compare our results with the power-efficiency trade-off relation recently proposed for the Markovian quantum Otto engine. We find that the power of our non-Markovian engine for a given efficiency value falls below the Markovian power-efficiency bound.