Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator

Abstract

I formulate a quantum stochastic thermodynamics for the quantum trajectories of a continuously-monitored forced harmonic oscillator coupled to a thermal reservoir. Consistent trajectory-dependent definitions are introduced for work, heat, and entropy, through engineering the thermal reservoir from a sequence of two-level systems. Within this formalism the connection between irreversibility and entropy production is analyzed and confirmed by proving a detailed fluctuation theorem for quantum trajectories. Finally, possible experimental verifications are discussed.

16 pages, 3 figures, submitted to PRE; expanded introduction and conclusion, corrected typos, new figure 3

References in corpus (29)

• Fluctuation theorems: Work is not an observable
• A Straightforward Introduction to Continuous Quantum Measurement
• Dissipation: The phase-space perspective
• The second law, Maxwell's daemon and work derivable from quantum heat engines
• Fluctuation theorems for stochastic dynamics
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Rare events and the convergence of exponentially averaged work values
• Stochastic thermodynamics of chemical reaction networks
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Quantum Operation Time Reversal
• Measurement of Stochastic Entropy Production
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Distribution of Entropy Production for a Colloidal Particle in a Nonequilibrium Steady State
• Microcanonical quantum fluctuation theorems
• Influence of measurements on the statistics of work performed on a quantum system
• Quantum jumps and entropy production
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Statistics of work performed on a forced quantum oscillator
• Entropy production for mechanically or chemically driven biomolecules
• The "footprints'' of irreversibility
• Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Steady state fluctuations of the dissipated heat for a quantum stochastic model
• Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
• Microscopic heat from the energetics of stochastic phenomena
• Model Studies on the Quantum Jarzynski Relation
• Symmetry Relations for Trajectories of a Brownian Motor
• Observing different quantum trajectories in cavity QED

Cited by in corpus (118)

• Non-Hermitian Physics
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Quantum collision models: open system dynamics from repeated interactions
• The role of quantum measurement in stochastic thermodynamics
• Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments
• Non-equilibrium quantum fluctuations of work
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Entropy production along nonequilibrium quantum jump trajectories
• Speed limit for open quantum systems
• Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Periodic Thermodynamics of Open Quantum Systems
• Qubit models of weak continuous measurements
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Thermodynamics of discrete quantum processes
• The Schrödinger-Langevin equation with and without thermal fluctuations
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Repeated interactions and quantum stochastic thermodynamics at strong coupling
• The quantum-classical correspondence principle for work distributions
• Thermodynamics of Gambling Demons
• Assessing the non-equilibrium thermodynamics in a quenched quantum many-body system via single projective measurements
• Path integral approach to quantum thermodynamics
• Integral Quantum Fluctuation Theorems under Measurement and Feedback control
• Quantum fluctuations hinder finite-time information erasure near the Landauer limit
• The squeezed thermal reservoir as a generalized equilibrium reservoir
• Thermodynamics of weakly measured quantum systems
• Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence
• An operational approach to quantum stochastic thermodynamics
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Periodic energy transport and entropy production in quantum electronics
• Stochastic thermodynamics of rapidly driven systems
• Heat and work along individual trajectories of a quantum bit
• Exchange Fluctuation Theorem for correlated quantum systems
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Work as an external quantum observable and an operational quantum work fluctuation theorem
• Measurement-based quantum heat engine in a multilevel system
• Stochastic Quantum Zeno by Large Deviation Theory
• Quantum nonequilibrium equalities with absolute irreversibility
• Steering heat engines: a truly quantum Maxwell demon
• Effects of Quantum Coherence on Work Statistics
• Characteristic Functions Based on Quantum Jump Trajectory
• Quantum entropy production in phase space
• Equivalent definitions of the quantum nonadiabatic entropy production
• Work and Efficiency of Quantum Otto Cycles in Power Law Trapping Potentials
• Entropy Production in Continuously Measured Gaussian Quantum Systems
• Work measurement in an optomechanical quantum heat engine
• Quantum Work in the Bohmian framework
• Quantum Martingale Theory and Entropy Production
• Thermodynamics of Quantum-Jump-Conditioned Feedback Control
• Probing quantum fluctuation theorems in engineered reservoirs
• Stochastic thermodynamics of quantum maps with and without equilibrium
• Quantum fluctuation theorems and power measurements
• Path integral approach to heat in quantum thermodynamics
• An autonomous quantum machine to measure the thermodynamic arrow of time
• Fluctuation Theorems for Continuous Quantum Measurement and Absolute Irreversibility
• Quantum Fluctuation Theorems
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
• Fundamental bounds on precision and response for quantum trajectory observables
• Quantum jump model for a system with a finite-size environment
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Joint statistics of work and entropy production along quantum trajectories
• Quantum Thermodynamics for Driven Dissipative Bosonic Systems
• Informational steady-states and conditional entropy production in continuously monitored systems
• Studying rare nonadiabatic dynamics with transition path sampling quantum jump trajectories
• Quantum work statistics of charged Dirac particles in time-dependent fields
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Quantum Fluctuation Theorem under Continuous Measurement and Feedback
• A Landau-Zener Lindblad equation and work extraction from coherences
• Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality
• Quantum master equations for entangled qubit environments
• Fluctuation-dissipation theorem for non-equilibrium quantum systems
• Non-equilibrium thermodynamics of continuously measured quantum systems: a circuit-QED implementation
• Characterizing a statistical arrow of time in quantum measurement dynamics
• Conditional work statistics of quantum measurements
• Work fluctuation-dissipation trade-off in heat engines
• Thermodynamics of a continuously monitored double quantum dot heat engine in the repeated interactions framework
• Entropy production and fluctuation theorems in a continuously monitored optical cavity at zero temperature
• Calculating work in weakly driven quantum master equations: backward and forward equations
• Fluctuation theorems in feedback-controlled open quantum systems: quantum coherence and absolute irreversibility
• A quantum fluctuation theorem for any Lindblad master equation
• One qubit and one photon -- the simplest polaritonic heat engine
• Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks
• Stochastic Floquet quantum heat engines and stochastic efficiencies
• Thermalization processes induced by quantum monitoring in multi-level systems
• Macroscopic realism of quantum work fluctuations
• Fluctuations and stability of a fast driven Otto cycle
• Semi-Markov processes in open quantum systems: Connections and applications in counting statistics
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Enantiomer detection via Quantum Otto cycle
• Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator
• Work, heat and entropy production along quantum trajectories
• Dissipation in the Generalized Gibbs Ensemble
• Work fluctuation and total entropy production in nonequilibrium processes
• Nonequilibrium work equalities in isolated quantum systems
• Force-current structure in Markovian open quantum systems and its applications: geometric housekeeping-excess decomposition and thermodynamic trade-off relations
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Quantum motion with trajectories: beyond the Gaussian beam approximation
• Contributions to single-shot energy exchanges in open quantum systems
• Collisional-model quantum trajectories for entangled qubit environments
• Calorimetric measurement of work for a driven harmonic oscillator
• The EPR Paradox Implies A Minimum Achievable Temperature
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• On a tilted Liouville-master equation of open quantum systems
• Quantifying athermality and quantum induced deviations from classical fluctuation relations
• Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes
• Auxiliary open quantum system for the Floquet quantum master equation
• Operational work fluctuation theorem for open quantum systems
• Noninvasive and nonadiabatic quantum Maxwell demon
• A fluctuation theorem for Floquet quantum master equations
• Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems
• Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum
• Quantum thermodynamics under continuous monitoring: a general framework
• The Coherent Crooks Equality
• Fluctuation theorem in cavity quantum electrodynamics systems