Fluctuations of work in nearly adiabatically driven open quantum systems

Abstract

We extend the quantum jump method to nearly adiabatically driven open quantum systems in a way that allows for an accurate account of the external driving in the system-environment interaction. Using this framework, we construct the corresponding trajectory-dependent work performed on the system and derive the integral fluctuation theorem and the Jarzynski equality for nearly adiabatic driving. We show that such identities hold as long as the stochastic dynamics and work variable are consistently defined. We numerically study the emerging work statistics for a two-level quantum system and find that the conventional diabatic approximation is unable to capture some prominent features arising from driving such as the continuity of the probability density of work. Our results reveal the necessity of using accurate expressions for the drive-dressed heat exchange in future experiments probing jump time distributions.

arXiv comment15 pages, 5 figures

References in corpus (54)

• A nonequilibrium equality for free energy differences
• Introduction to Quantum Noise, Measurement and Amplification
• 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
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Fluctuation theorems: Work is not an observable
• Experimental realization of a Szilard engine with a single electron
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
• Experimental study of mutual information in a Maxwell Demon
• Measuring the characteristic function of the work distribution
• Nonequilibrium entropy production for open quantum systems
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Non-equilibrium quantum fluctuations of work
• Employing trapped cold ions to verify the quantum Jarzynski equality
• 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
• Entropy production along nonequilibrium quantum jump trajectories
• Distribution of Entropy Production in a Single-Electron Box
• Measurement quantum mechanics and experiments on quantum Zeno effect
• Fluctuation theorems for quantum processes
• Coherent oscillations in a superconducting multi-level quantum system
• Quantum work relations and response theory
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Local effective dynamics of quantum systems: A generalized approach to work and heat
• A Quantum Analogue of the Jarzynski Equality
• Microcanonical quantum fluctuation theorems
• Jarzynski equality for quantum stochastic maps
• Non-equilibrium equalities with unital quantum channels
• Decoherence in adiabatic quantum evolution - application to Cooper pair pumping
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Heat-exchange statistics in driven open quantum systems
• The Crooks relation in optical spectra - universality in work distributions for weak local quenches
• Work and its fluctuations in a driven quantum system
• Entropy production and information fluctuations along quantum trajectories
• Quantum fluctuation theorems and generalized measurements during the force protocol
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Decoherence of adiabatically steered quantum systems
• Exact fluctuation theorem without ensemble quantities
• Equivalent definitions of the quantum nonadiabatic entropy production
• Heat due to system-reservoir correlations in thermal equilibrium
• Moments of work in the two-point measurement protocol for a driven open quantum system
• Quantum driving and work
• Conservation law of operator current in open quantum systems
• 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
• Quantum Fluctuation Relations for Ensembles of Wave Functions
• Adiabatically steered open quantum systems: Master equation and optimal phase
• Superadiabatic theory for Cooper pair pumping under decoherence
• Fluctuation Theorems and the Generalised Gibbs Ensemble in Integrable Systems

Cited by in corpus (18)

• Fully quantum fluctuation theorems
• Nonequilibrium potential and fluctuation theorems for quantum maps
• The quantum-classical correspondence principle for work distributions
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Effects of Quantum Coherence on Work Statistics
• Characteristic Functions Based on Quantum Jump Trajectory
• Work measurement in an optomechanical quantum heat engine
• Quantum jump model for a system with a finite-size environment
• Entropy production and fluctuations in a Maxwell's refrigerator with squeezing
• Calculating work in weakly driven quantum master equations: backward and forward equations
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Quantum Treatment for Bose-Einstein Condensation in Non-Equilibrium Systems
• Quantum work statistics at strong reservoir coupling
• Path integral approach to the calculation of the characteristic function of work
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system
• Calorimetric measurement of work for a driven harmonic oscillator
• Quantum thermodynamics under continuous monitoring: a general framework