Optimal thermodynamic control in open quantum systems

Abstract

We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes which minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.

11 pages, 5 figures; corrected typos, added references, all results unchanged

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Cited by in corpus (30)

• Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
• Optimal cycles for low-dissipation heat engines
• Thermodynamic length in open quantum systems
• Identifying optimal cycles in quantum thermal machines with reinforcement-learning
• Spin quantum heat engines with shortcuts to adiabaticity
• Optimal Control Methods for Quantum Batteries
• Geometric optimisation of quantum thermodynamic processes
• Non-Markov Enhancement of Maximum Power for Quantum Thermal Machines
• Maximum power and corresponding efficiency for two-level heat engines and refrigerators: optimality of fast cycles
• Geometry of work fluctuations versus efficiency in microscopic thermal machines
• The Ising critical quantum Otto engine
• Geometrical bounds on irreversibility in open quantum systems
• Pareto-optimal cycles for power, efficiency and fluctuations of quantum heat engines using reinforcement learning
• Differentiable Molecular Simulations for Control and Learning
• Quantum Fokker-Planck Master Equation for Continuous Feedback Control
• Maximum power heat engines and refrigerators in the fast-driving regime
• Two-Stroke Optimization Scheme for Mesoscopic Refrigerators
• Comparison between optimal control and shortcut to adiabaticity protocols in a linear control system
• Extrapolating the thermodynamic length with finite-time measurements
• Double quantum-dot engine fueled by entanglement between electron spins
• Optimal protocols and universal time-energy bound in Brownian thermodynamics
• Quantum jump approach to microscopic heat engines
• Variational approach to the optimal control of coherently driven, open quantum system dynamics
• Dynamical invariant based shortcut to equilibration in open quantum systems
• Optimal finite-time heat engines under constrained control
• Optimizing Brownian heat engine with shortcut strategy
• Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning
• Optimal control of dissipation and work fluctuations for rapidly driven systems
• Exploring the Optimal Cycle for Quantum Heat Engine using Reinforcement Learning
• Coherent dynamical control of quantum processes