Fluctuation theorems for quantum master equations

Abstract

A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i.e. a quantum master equation (QME). Quantum trajectories and their associated entropy, heat and work appear naturally by transforming the QME to a time dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady state fluctuation theorem and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.

Submitted to Phys. Rev. E

Cited by in corpus (109)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum Thermodynamics
• Fluctuation theorems for stochastic dynamics
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Fluctuation Theorems
• Nonequilibrium Thermodynamics of Feedback Control
• Quantum Szilard Engine
• Entropy production and the arrow of time
• Nonequilibrium entropy production for open quantum systems
• Hierarchy of stochastic pure states for open quantum system dynamics
• Fluctuation theorem for currents in open quantum systems
• Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
• Quantum work and the thermodynamic cost of quantum measurements
• Fluctuation theorems in driven open quantum systems
• Fully quantum fluctuation theorems
• Thermodynamics of discrete quantum processes
• Quantum work relations and response theory
• Driven Spin Systems as Quantum Thermodynamic Machines: Fundamental Limits
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Fluctuation theorem for counting-statistics in electron transport through quantum junctions
• Microcanonical quantum fluctuation theorems
• Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence
• An operational approach to quantum stochastic thermodynamics
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Statistics of work performed on a forced quantum oscillator
• Detection of single-electron heat transfer statistics
• Work and its fluctuations in a driven quantum system
• Quantum Coherence in a Quantum Heat Engine
• Entropy production and information fluctuations along quantum trajectories
• Interference effects in the counting statistics of electron transfers through a double quantum dot
• Thermodynamics and Fluctuation Theorems for a Strongly Coupled Open Quantum System: An Exactly Solvable Case
• Fluctuations of Quantum Currents and Unravelings of Master Equations
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Characteristic Functions Based on Quantum Jump Trajectory
• Dynamics and thermodynamics of a central spin immersed in a spin bath
• Geometric Heat Pump: Controlling Thermal Transport with Time-dependent Modulations
• Quantum Work in the Bohmian framework
• Work measurement in an optomechanical quantum heat engine
• Thermodynamics of Quantum-Jump-Conditioned Feedback Control
• Jarzynski Equality for Driven Quantum Field Theories
• Work fluctuations for Bose particles in grand canonical initial states
• Quantum fluctuation theorems and power measurements
• Work fluctuations in quantum spin chains
• Quantum driving and work
• Lead Geometry and Transport Statistics in Molecular Junctions
• Energy transport between two pure-dephasing reservoirs
• Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Typical and extreme entropies of long-lived isolated quantum systems
• Quantum jump model for a system with a finite-size environment
• A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems
• Fluctuation theorems for non-Markovian quantum processes
• Quantum Fluctuation Relations for Ensembles of Wave Functions
• Nonequilibrium work statistics of an Aharonov-Bohm flux
• Time-dependent magnetotransport in an interacting double quantum wire with window coupling
• Quantum free energy differences from non-equilibrium path integrals: II. Convergence properties for the harmonic oscillator
• Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions
• Model Studies on the Quantum Jarzynski Relation
• Quantum free energy differences from non-equilibrium path integrals: I. Methods and numerical application
• Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Optimal processes for probabilistic work extraction beyond the second law
• Thermodynamic utility of Non-Markovianity from the perspective of resource interconversion
• An atomic symmetry-controlled thermal switch
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Numerically "exact" simulations of entropy production in the fully quantum regime: Boltzmann entropy versus von Neumann entropy
• Revisiting the quantum Szilard engine with fully quantum considerations
• A test of "fluctuation theorem" in non-Markovian open quantum systems
• Transient fluctuation theorem in closed quantum systems
• Electron transport through a quantum dot assisted by cavity photons
• Macroscopically deterministic, Markovian thermalization in finite quantum spin systems
• Calculating work in weakly driven quantum master equations: backward and forward equations
• The characteristic functions of quantum heat with baths at different temperatures
• Fluctuation theorems in feedback-controlled open quantum systems: quantum coherence and absolute irreversibility
• Non-adiabatic effect in quantum pumping for a spin-boson system
• A quantum fluctuation theorem for any Lindblad master equation
• The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach
• Clausius inequality versus quantum coherence
• Energetic fluctuations in an open quantum process
• Fluctuation theorem for entropy production during effusion of a relativistic ideal gas
• Semi-Markov processes in open quantum systems: Connections and applications in counting statistics
• Semi-classical work and quantum work identities in Weyl representation
• Extracting work from the magnetic field coupled Brownian particles
• Entropy production for complex Langevin equations
• General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. I. Theoretical Formulation
• Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum
• Nonequilibrium work equalities in isolated quantum systems
• Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Force-current structure in Markovian open quantum systems and its applications: geometric housekeeping-excess decomposition and thermodynamic trade-off relations
• The Minimal Modal Interpretation of Quantum Theory
• Gauge invariance and geometric phase in nonequilibrium thermodynamics
• Calorimetric measurement of work for a driven harmonic oscillator
• Microscopic analysis of the microscopic reversibility in quantum systems
• Transport fluctuation relations in interacting quantum pumps
• Transient State Work Fluctuation Theorem for a Driven Classical System
• Fluctuation relation in continuous-time random walks driven by an external field
• The distribution of work performed on a NIS junction
• Work statistics in the periodically driven quartic oscillator: classical versus quantum dynamics
• Quasiprobability Thermodynamic Uncertainty Relation
• Many-body work distributions
• Measurement and Quantum Dynamics in the Minimal Modal Interpretation of Quantum Theory
• Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field
• Projection hypothesis in the setting for the quantum Jarzynski equality
• Derivation of a linear collision operator for the spinorial Wigner equation and its semiclassical limit
• Calculation of semiclassical free energy differences along non-equilibrium classical trajectories
• On the Quantum Jarzynski Identity