The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance

Abstract

We study the thermodynamics of a quantum system interacting with different baths in the repeated interaction framework. In an appropriate limit, the evolution takes the Lindblad form and the corresponding thermodynamic quantities are determined by the state of the full system plus baths. We identify conditions under which the thermodynamics of the open system can be described only by system properties and find a quantum local detailed balance condition with respect to an equilibrium state that may not be a Gibbs state. The three-qubit refrigerator introduced in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett.$105$, 130401 (2010)] is an example of such a system. From a repeated interaction microscopic model we derive the Lindblad equation that describes its dynamics and discuss its thermodynamic properties for arbitrary values of the internal coupling between the qubits. We find that external power (proportional to the internal coupling strength) is required to bring the system to its steady state, but once there, it works autonomously as discussed in [N. Linden, S. Popescu and P. Skrzypczyk, Phys. Rev. Lett. $105$, 130401 (2010)].

11 pages, 2 figures

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• Markovian Master Equations: A Critical Study
• Modeling heat transport through completely positive maps
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Performance bound for quantum absorption refrigerators
• Autonomous Quantum Refrigerator in a Circuit-QED Architecture Based on a Josephson Junction

Cited by in corpus (11)

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• Quantum thermal absorption machines: refrigerators, engines and clocks
• Thermodynamics of precision in quantum nano-machines
• Nonequilibrium Dynamics with Finite-Time Repeated Interactions
• Local master equations bypass the secular approximation
• Pushing the limits of the reaction-coordinate mapping
• Wigner entropy production and heat transport in linear quantum lattices
• Efficiency fluctuations in a quantum battery charged by a repeated interaction process
• Cooling condition for multilevel quantum absorption refrigerators
• Designing Robust Quantum Refrigerators in Disordered Spin Models
• Three qubits in less than three baths: Beyond two-body system-bath interactions in quantum refrigerators