Bosonic two-stroke heat engines with polynomial nonlinear coupling

Abstract

We study the thermodynamics of two-stroke heat engines where two bosonic modes $a$ and $b$ are coupled by the general nonlinear interaction $V_{\theta }=\exp (\theta a^{†n}{b}^m-{\theta }^{\ast }{a}^n{b}^{†m})$. By adopting the two-point measurement scheme we retrieve the distribution of the stochastic work, and hence the relative fluctuations of the extracted work up to the second order in the coupling $\theta$. We identify the optimal interactions providing large average work with small fluctuations in the operational regime of the heat engine. Then, we consider the specific cases $n=2$, $m=1$ and $n=1$, $m=2$ up to the fourth order in $\theta$. We optimize the average work and the signal-to-noise ratio over the frequencies of the bosonic modes and the temperatures of the reservoirs. Finally, we determine the thermodynamic uncertainty relations for these processes in relation with the order of the expansion of the unitary interaction $V_{\theta }$.

22 pages, 14 figures

References in corpus (29)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Thermodynamic uncertainty relation for biomolecular processes
• Quantum Thermodynamic Cycles and quantum heat engines
• Fluctuation theorems: Work is not an observable
• Dissipation bounds all steady-state current fluctuations
• Maximal work extraction from quantum systems
• Irreversible entropy production, from quantum to classical
• Colloquium: Quantum Batteries
• Fluctuation theorem uncertainty relation
• Finite-time generalization of the thermodynamic uncertainty relation
• Thermodynamic uncertainty relations from exchange fluctuation theorems
• Discrete-time thermodynamic uncertainty relation
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Work extremum principle: Structure and function of quantum heat engines
• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
• Thermodynamic uncertainty relations including measurement and feedback
• A quantum version of free energy - irreversible work relations
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Stroboscopic two-stroke quantum heat engines
• Thermodynamic Uncertainty Relations for Bosonic Otto Engines
• Multilevel quantum thermodynamic swap engines
• Fluctuation theorems and thermodynamic uncertainty relations
• Quantum thermodynamics of two bosonic systems
• Thermodynamic uncertainty relation from involutions
• Catalytic enhancement in the performance of the microscopic two-stroke heat engine
• Quantum second harmonic generation in terms of elementary processes
• Work Fluctuations in Ergotropic Heat Engines
• Evading Thermodynamic Uncertainty Relations via Asymmetric Dynamic Protocols