Nonequilibrium work equalities in isolated quantum systems

Abstract

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, which includes the origin of the equalities, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, the recent experimental verifications. Some results are given here first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which shall be useful in understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

1 figure

References in corpus (74)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Nonequilibrium dynamics of closed interacting quantum systems
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• Artificial Brownian motors: Controlling transport on the nanoscale
• 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
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Fluctuation theorem for stochastic dynamics
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• Dynamical ensembles in stationary states
• Steady State Thermodynamics of Langevin Systems
• Fluctuation theorems: Work is not an observable
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• The Nonequilibrium Thermodynamics of Small Systems
• Generalized Jarzynski Equality under Nonequilibrium Feedback Control
• Dissipation: The phase-space perspective
• The Fluctuation Theorem as a Gibbs Property
• Three detailed fluctuation theorems
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
• Fluctuation Theorems
• Measuring the characteristic function of the work distribution
• Entropy production and the arrow of time
• Nonequilibrium entropy production for open quantum systems
• Fluctuation theorem for currents in open quantum systems
• Comparison of far-from-equilibrium work relations
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Fluctuation theorem in quantum heat conduction
• Integral fluctuation theorem for the housekeeping heat
• Nonequilibrium work distribution of a quantum harmonic oscillator
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Quantum jump approach for work and dissipation in a two-level system
• Dissipation and lag in irreversible processes
• Fluctuation theorems for quantum master equations
• Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
• Fluctuation Relations for Diffusion Processes
• Entropy production along nonequilibrium quantum jump trajectories
• Quantum Operation Time Reversal
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Fluctuation theorems for quantum processes
• A quantum version of free energy - irreversible work relations
• Quantum work relations and response theory
• Quantum Fluctuation Relations for the Lindblad Master Equation
• A Quantum Analogue of the Jarzynski Equality
• Microcanonical quantum fluctuation theorems
• Work probability distribution in systems driven out of equilibrium
• Comparison of work fluctuation relations
• Non-equilibrium equalities with unital quantum channels
• Employing Circuit QED to Measure Nonequilibrium Work Fluctuations
• Jarzynski equation for a simple quantum system: Comparing two definitions of work
• Statistics of work performed on a forced quantum oscillator
• Universal energy fluctuations in thermally isolated driven systems
• The Crooks relation in optical spectra - universality in work distributions for weak local quenches
• Entropy production and information fluctuations along quantum trajectories
• Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models
• Fluctuations of Quantum Currents and Unravelings of Master Equations
• Quantum Bochkov-Kuzovlev Work Fluctuation Theorems
• Validity of nonequilibrium work relations for the rapidly expanding quantum piston
• Steady state fluctuations of the dissipated heat for a quantum stochastic model
• Work probability distribution in single molecule experiments
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Transient quantum fluctuation theorems and generalized measurements
• Quantum fluctuation theorem: Can we go from micro to meso?
• Derivation of quantum work equalities using quantum Feynman-Kac formula
• A generalized integral fluctuation theorem for diffusion processes
• Work and heat probability distributions in out-of-equilibrium systems
• Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view

Cited by in corpus (5)

• Optimal protocols for slowly-driven quantum processes
• Characteristic Functions Based on Quantum Jump Trajectory
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Calculating work in weakly driven quantum master equations: backward and forward equations
• Statistics of work done in degenerate parametric amplification process