Characteristic Functions Based on Quantum Jump Trajectory

Abstract

Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A conventional procedure for obtaining these functions is to resort to a first-principles approach; namely, the evolution equations of the CFs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system. However, the QMEs can be unraveled by a quantum jump trajectory. Thermodynamic quantities such as the heat, work, and entropy production can be well defined along a trajectory. Hence, on the basis of the notion of a trajectory, can we straightforwardly derive these CFs, e.g., their evolution equations? This is essential to establish the self-contained stochastic thermodynamics of a QME. In this paper, we show that it is indeed plausible and also simple. Particularly, these equations are fully consistent with those obtained by the first-principles method. Our results have practical significance; they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments.

1 figure. Accepted by Phys. Rev. E

References in corpus (70)

• A nonequilibrium equality for free energy differences
• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Fluctuation theorem for stochastic dynamics
• Path ensembles averages in systems driven far-from-equilibrium
• Quantum trajectories and open many-body quantum systems
• Open Quantum Systems. An Introduction
• Quantum Thermodynamics
• Quantum annealing with more than one hundred qubits
• Steady State Thermodynamics of Langevin Systems
• Fluctuation theorems: Work is not an observable
• Dissipation: The phase-space perspective
• The Fluctuation Theorem as a Gibbs Property
• Observing single quantum trajectories of a superconducting qubit
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• Non-Markovian quantum jumps
• Thermodynamics of Quantum Jump Trajectories
• Quantum Adiabatic Markovian Master Equations
• Tracking Photon Jumps with Repeated Quantum Non-Demolition Parity Measurements
• Comparison of far-from-equilibrium work relations
• Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
• Genuine quantum trajectories for non-Markovian processes
• Quantum jump approach for work and dissipation in a two-level system
• Fluctuation theorems for quantum master equations
• Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
• Non-Poissonian Quantum Jumps of a Fluxonium Qubit due to Quasiparticle Excitations
• Entropy production along nonequilibrium quantum jump trajectories
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Quantum Operation Time Reversal
• Fluctuation theorems in driven open quantum systems
• Markovian Master Equation and Thermodynamics of Two-level System in Strong Laser Field
• Observing quantum state diffusion by heterodyne detection of fluorescence
• Nonequilibrium potential and fluctuation theorems for quantum maps
• A quantum version of free energy - irreversible work relations
• Quantum work relations and response theory
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Dynamic entanglement in oscillating molecules and potential biological implications
• A Quantum Analogue of the Jarzynski Equality
• The quantum-classical correspondence principle for work distributions
• Thermodynamics of weakly measured quantum systems
• Exact large-deviation statistics for a nonequilibrium quantum spin chain
• Quantum jumps and entropy production
• Heat-exchange statistics in driven open quantum systems
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Stochastic thermodynamics of rapidly driven systems
• Entropy production and information fluctuations along quantum trajectories
• Energy flow in periodic thermodynamics
• Fluctuations of Quantum Currents and Unravelings of Master Equations
• Entropic fluctuations of quantum dynamical semigroups
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Physical interpretation of stochastic Schroedinger equations in cavity QED
• Moments of work in the two-point measurement protocol for a driven open quantum system
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Quantum fluctuation theorem: Can we go from micro to meso?
• A generic map from non-Lindblad to Lindblad master equations
• Master Equations for pulsed magnetic fields: Application to magnetic molecules
• Derivation of quantum work equalities using quantum Feynman-Kac formula
• Calculating work in weakly driven quantum master equations: backward and forward equations
• Work and heat probability distributions in out-of-equilibrium systems
• Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks
• Nonequilibrium work equalities in isolated quantum systems

Cited by in corpus (21)

• Non-Hermitian Physics
• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Work fluctuations in slow processes: quantum signatures and optimal control
• Thermodynamics of Gambling Demons
• Effects of Quantum Coherence on Work Statistics
• Reconstructing quantum entropy production to probe irreversibility and correlations
• A quantum fluctuation theorem for any Lindblad master equation
• Stochastic Floquet quantum heat engines and stochastic efficiencies
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Semi-Markov processes in open quantum systems: Connections and applications in counting statistics
• Work statistics and thermal phase transitions
• Quantum work statistics at strong reservoir coupling
• Contributions to single-shot energy exchanges in open quantum systems
• On a tilted Liouville-master equation of open quantum systems
• Auxiliary open quantum system for the Floquet quantum master equation
• Semi-Markov Processes in Open Quantum Systems. II. Counting Statistics with Resetting
• Asymptotic Large Deviations of Counting Statistics in Open Quantum Systems
• Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum
• Response kinetic uncertainty relation for Markovian open quantum systems
• A fluctuation theorem for Floquet quantum master equations
• Quantum thermodynamics under continuous monitoring: a general framework