Precision bound and optimal control in periodically modulated continuous quantum thermal machines

Abstract

We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the Chopped Random Basis (CRAB) optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator, and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.

arXiv comment17 pages, 6 figures. Close to published version

References in corpus (74)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Thermodynamic uncertainty relation for biomolecular processes
• Quantum Thermodynamics
• Quantum Thermodynamics
• Dissipation bounds all steady-state current fluctuations
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Optimal control technique for Many Body Quantum Systems dynamics
• Universal trade-off between power, efficiency, and constancy in steady-state heat engines
• Chopped random-basis quantum optimization
• The quantum harmonic Otto cycle
• Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents
• Universal bounds on current fluctuations
• Finite-time generalization of the thermodynamic uncertainty relation
• Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
• Current fluctuations and transport efficiency for general Langevin systems
• Discrete-time thermodynamic uncertainty relation
• Thermodynamics of precision in quantum non equilibrium steady states
• Unravelling the large deviation statistics of Markovian open quantum systems
• Cost and Precision of Brownian Clocks
• Thermodynamic uncertainty relation for time-dependent driving
• Minimal universal quantum heat machine
• Inferring dissipation from current fluctuations
• Cycling tames power fluctuations near optimum efficiency
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• Unified thermodynamic uncertainty relations in linear response
• Thermodynamics of quantum systems under dynamical control
• On the validity of the thermodynamic uncertainty relation in quantum systems
• A Discrete Four Stroke Quantum Heat Engine Exploring the Origin of Friction
• Quantum thermodynamic uncertainty relation for continuous measurement
• Tightening the uncertainty principle for stochastic currents
• One decade of quantum optimal control in the chopped random basis
• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Stochastic thermodynamics: From principles to the cost of precision
• Thermodynamic uncertainty relation for general open quantum systems
• Coherence-enhanced constancy of a quantum thermoelectric generator
• Thermodynamic Uncertainty Relation for Arbitrary Initial States
• Markovian Master Equation and Thermodynamics of Two-level System in Strong Laser Field
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Thermodynamic uncertainty relations including measurement and feedback
• Bounds on current fluctuations in periodically driven systems
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Speeding up and slowing down the relaxation of a qubit by optimal control
• Entropic bounds on currents in Langevin systems
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• A generalization of the thermodynamic uncertainty relation to periodically driven systems
• Uncertainty relations for underdamped Langevin dynamics
• Concepts of work in autonomous quantum heat engines
• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• Heat-exchange statistics in driven open quantum systems
• Enhanced precision bound of low-temperature quantum thermometry via dynamical control
• Effect of a magnetic field on the thermodynamic uncertainty relation
• Violation of TUR in a periodically driven work-to-work converter from weak to strong dissipation
• Thermodynamics of precision in quantum nano-machines
• Thermodynamic uncertainty relations under arbitrary control protocols
• Universal Bounds on Fluctuations in Continuous Thermal Machines
• Experimental study of the thermodynamic uncertainty relation
• From quantum heat engines to laser cooling: Floquet theory beyond the Born-Markov approximation
• A quantum enhanced finite-time Otto cycle
• Thermodynamic uncertainty relations for coherently driven open quantum systems
• Thermodynamic Uncertainty Relations for Bosonic Otto Engines
• Mapping of uncertainty relations between continuous and discrete time
• Thermodynamic uncertainty relation for underdamped Langevin systems driven by a velocity-dependent force
• Bounds on fluctuations for finite-time quantum Otto cycle
• On the complexity of controlling quantum many-body dynamics
• A unifying picture of generalized thermodynamic uncertainty relations
• Two-Particle Interference with Double Twin-Atom Beams
• Environment-governed dynamics in driven quantum systems
• Thermodynamic uncertainty relation for energy transport in transient regime -- Model study
• Speed and Efficiency Limits of Multilevel Incoherent Heat Engines
• Quantumness and thermodynamic uncertainty relation of finite-time Otto cycle
• Optimal energy conversion through anti-adiabatic driving breaking time-reversal symmetry
• Engineering a thermal squeezed reservoir by system energy modulation
• The origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

Cited by in corpus (9)

• Fundamental bounds on precision and response for quantum trajectory observables
• Synchronization-induced violation of thermodynamic uncertainty relations
• Collective effects enhanced multi-qubit information engines
• Power-efficiency trade-off for finite-time quantum harmonic Otto heat engine via phase-space approach
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory
• Quasiprobability Thermodynamic Uncertainty Relation
• Response kinetic uncertainty relation for Markovian open quantum systems
• Information-thermodynamic bounds on precision in interacting quantum systems
• Universal Precision Limits in General Open Quantum Systems