Colloquium: Quantum fluctuation relations: Foundations and applications

Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars the reader is guided through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)linear response theory. A number of fundamental issues are clarified which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.

• Publication year

  2010

• Venue

  Reviews of Modern Physics

• Publication date

  2010-12-10

• Fields of study

  Physics

• Identifiers
  DOI 10.1103/RevModPhys.83.771arXiv 1012.2268
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Influence of measurements on the statistics of work performed on a quantum system.

  2011cited by this paper
• Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling

  2011cited by this paper
• Jarzynski Equality for an Energy-Controlled System (Proceedings of nanoPHYS'11)

  2011cited by this paper
• Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale

  2011cited by this paper
• Jarzynski Equality for an Energy-Controlled System

  2011cited by this paper
• Fluctuation theorem and microreversibility in a quantum coherent conductor

  2011cited by this paper
• Berry-phase-induced heat pumping and its impact on the fluctuation theorem.

  2010cited by this paper
• Generalized clausius inequality for nonequilibrium quantum processes.

  2010cited by this paper
• Quantum Jarzynski-Sagawa-Ueda Relations

  2010cited by this paper
• Thermodynamic anomalies in open quantum systems: Strong coupling effects in the isotropic XY model

  2010influential reference
• Quantum ground state and single-phonon control of a mechanical resonator

  2010cited by this paper
• Quantum annealing with Jarzynski equality

  2010cited by this paper
• Quantum work statistics of linear and nonlinear parametric oscillators

  2010cited by this paper
• Fluctuation theorems for continuously monitored quantum fluxes.

  2010influential reference
• Quantum Bochkov–Kuzovlev work fluctuation theorems

  2010influential reference
• Erratum: Fluctuation theorem for currents in open Quantum systems (New Journal of Physics (2009) 11 (043014))

  2009influential reference
• The work-Hamiltonian connection and the usefulness of the Jarzynski equality for free energy calculations.

  2009cited by this paper
• Generalized Jarzynski equality under nonequilibrium feedback control.

  2009cited by this paper
• Comment on "On the Crooks fluctuation theorem and the Jarzynski equality" [J. Chem. Phys. 129, 091101 (2008)].

  2009cited by this paper
• Synthesizing arbitrary quantum states in a superconducting resonator

  2009influential reference
• Bidirectional single-electron counting and the fluctuation theorem

  2009influential reference
• Detecting entanglement with Jarzynski's equality

  2009cited by this paper
• Near-field cavity optomechanics with nanomechanical oscillators

  2009cited by this paper
• Comment regarding "On the Crooks fluctuation theorem and the Jarzynski equality" [J. Chem. Phys. 129, 091101 (2008)] and "Nonequilibrium fluctuation-dissipation theorem of Brownian dynamics" [J. Chem. Phys. 129, 144113 (2008)].

  2009cited by this paper
• Fluctuation theorem for arbitrary open quantum systems.

  2009influential reference
• Nonequilibrium fluctuation relations in a quantum coherent conductor.

  2009influential reference
• FAST TRACK COMMUNICATION: Thermodynamics and fluctuation theorems for a strongly coupled open quantum system: an exactly solvable case

  2009influential reference
• Erratum: Statistics of work performed on a forced quantum oscillator [Phys. Rev. E 78, 011115 (2008)]

  2009cited by this paper
• On the Crooks fluctuation theorem and the Jarzynski equality

  2009cited by this paper
• Generalized fluctuation-dissipation theorem for steady-state systems.

  2009cited by this paper
• Comment regarding On the Crooks fluctuation theorem and the Jarzynski equality and Nonequilibrium fluctuation-dissipation theorem of Brownian dynamics

  2009cited by this paper
• Response to “Comment on ‘On the Crooks fluctuation theorem and the Jaraynski equality’ and ‘Nonequilibrium fluctuation dissipation theorem of Brownian dynamics’ [J. Chem. Phys. 130, 107101 (2009)]”

  2009cited by this paper
• Measuring the convergence of Monte Carlo free-energy calculations.

  2009cited by this paper
• The fluctuation theorem for currents in open quantum systems

  2008cited by this paper
• Fluctuation theorems in driven open quantum systems

  2008influential reference
• N ov 2 00 7 Information and entropy in quantum Brownian motion : Thermodynamic entropy versus von Neumann entropy

  2008cited by this paper
• Using bijective maps to improve free-energy estimates.

  2008cited by this paper
• On the work–Hamiltonian connection in manipulated systems

  2008cited by this paper
• Optimized free energies from bidirectional single-molecule force spectroscopy.

  2008cited by this paper
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems

  2008influential reference
• Comment on "Failure of the work-Hamiltonian connection for free-energy calculations".

  2008cited by this paper
• Generation of Fock states in a superconducting quantum circuit

  2008cited by this paper
• Cavity Optomechanics: Back-Action at the Mesoscale

  2008cited by this paper
• Statistics of work performed on a forced quantum oscillator.

  2008influential reference
• On the Crooks fluctuation theorem and the Jarzynski equality.

  2008cited by this paper
• Quantum work relations and response theory.

  2008influential reference
• Nonequilibrium fluctuation-dissipation theorem of Brownian dynamics.

  2008influential reference
• Employing trapped cold ions to verify the quantum Jarzynski equality.

  2008cited by this paper
• Escorted free energy simulations: improving convergence by reducing dissipation.

  2008cited by this paper
• Fluctuation-dissipation: Response theory in statistical physics

  2008cited by this paper
• Increase of Boltzmann entropy in a quantum forced harmonic oscillator.

  2008influential reference
• Nonequilibrium work relations : foundations and applications

  2008influential reference
• Vilar and Rubi Reply

  2008cited by this paper
• Approaching the Quantum Limit of a

  2008cited by this paper
• Nonequilibrium work relations: foundations and applications

  2008influential reference
• Comment on "Failure of the work-Hamiltonian connection for free-energy calculations".

  2007cited by this paper
• The Tasaki–Crooks quantum fluctuation theorem

  2007cited by this paper
• A fluctuation theorem for currents and non-linear response coefficients

  2007cited by this paper
• Fluctuation theorems: work is not an observable.

  2007influential reference
• Dissipation: the phase-space perspective.

  2007cited by this paper
• Fluctuation theorem in quantum heat conduction.

  2007cited by this paper
• Failure of the work-Hamiltonian connection for free-energy calculations.

  2007cited by this paper
• Comparison of work fluctuation relations

  2007cited by this paper
• Colloquium: The physics of Maxwell's demon and information

  2007cited by this paper
• Stochastic thermodynamics: principles and perspectives

  2007influential reference
• On the Jarzynski relation for dissipative quantum dynamics

  2007cited by this paper
• Microcanonical quantum fluctuation theorems.

  2007influential reference
• INVITED ARTICLE: Fluctuations in nonequilibrium statistical mechanics: models, mathematical theory, physical mechanisms

  2007cited by this paper
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field

  2007cited by this paper
• Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap

  2007influential reference
• Nonequilibrium work distribution of a quantum harmonic oscillator.

  2007influential reference
• QUANTUM BROWNIAN MOTION AND THE THIRD LAW OF THERMODYNAMICS

  2006cited by this paper
• Fluctuation theorems for quantum master equations.

  2006cited by this paper
• Comparison of far-from-equilibrium work relations

  2006cited by this paper
• Bidirectional Counting of Single Electrons

  2006cited by this paper
• Fluctuation and dissipation of work in a Joule experiment.

  2005cited by this paper
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies

  2005influential reference
• UvA-DARE ( Digital Academic Repository ) Fluctuations of work from quantum subensembles : The case against quantum work-fluctuation theorems

  2005cited by this paper
• An experimental test of the Jarzynski equality in a mechanical experiment

  2005influential reference
• Quantum Optics in Phase Space: SCHLEICH:QUANTUM OPTICS O-BK

  2005cited by this paper
• Eine neue Bestimmung der Moleküldimensionen

  2005cited by this paper
• Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)]

  2005cited by this paper
• Classical and quantum fluctuation theorems for heat exchange.

  2004influential reference
• Entropy and density of states from isoenergetic nonequilibrium processes.

  2004influential reference
• Fundamental aspects of quantum Brownian motion.

  2004cited by this paper
• Nonequilibrium work theorem for a system strongly coupled to a thermal environment

  2004cited by this paper
• Quantum extension of the Jarzynski relation: analogy with stochastic dephasing.

  2003cited by this paper
• Quantum version of free-energy--irreversible-work relations.

  2003cited by this paper
• Statistical thermodynamics of quantum Brownian motion: construction of perpetuum mobile of the second kind.

  2002cited by this paper
• Path Integrals and Their Application to Dissipative Quantum Systems

  2002cited by this paper
• Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality

  2002cited by this paper
• Targeted free energy perturbation.

  2001cited by this paper
• Quantum optics in phase space

  2001cited by this paper
• The role of relative entropy in quantum information theory

  2001cited by this paper
• A Quantum Fluctuation Theorem

  2000cited by this paper
• A Quantum Analogue of the Jarzynski Equality

  2000cited by this paper
• Jarzynski Relations for Quantum Systems and Some Applications

  2000cited by this paper
• Hamiltonian Derivation of a Detailed Fluctuation Theorem

  1999cited by this paper
• Response to “Comment on ‘The complete Schwarzschild interior and exterior solution in the harmonic coordinate system’ ” [J. Math. Phys. 40, 4177 (1999)]

  1999cited by this paper
• Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.

  1999cited by this paper

• Quantum Otto heat-engine with Kitaev-Heisenberg cluster: Possible roles of frustration, magnons, and duality

  2026cites this paper
• When Noise is the Signal [Measurement Methodology]

  2026cites this paper
• Signatures of coherent initial ensembles on all work moments

  2026cites this paper
• Irreversibility of decorrelating processes: an experimental assessment in cavity QED

  2026cites this paper
• An overview of continuous quantum measurements and its implications

  2026cites this paper
• Quantum regression theorem in the Unruh-DeWitt battery

  2026cites this paper
• Optimal Control to Minimize Dissipation and Fluctuations in Open Quantum Systems Beyond Slow and Rapid Regimes

  2026cites this paper
• Universal Thermodynamic Uncertainty Relation for Quantum $f-$Divergences

  2025cites this paper
• From Quantum-Mechanical Acceleration Limits to Upper Bounds on Fluctuation Growth of Observables in Unitary Dynamics

  2025cites this paper
• Adiabatic vacua from linear complex structures

  2025cites this paper
• Fisher information and fluctuations in quantum gas systems

  2025cites this paper
• Restoring the second law to classical-quantum dynamics

  2025cites this paper
• A framework for fluctuating times and counting observables in stochastic excursions

  2025cites this paper
• Full counting statistics for boundary driven transport in presence of correlated gain and loss channels

  2025cites this paper
• A friendly guide to exorcising Maxwell's demon

  2025cites this paper
• Fluctuation theorems with optical tweezers: theory and practice

  2025cites this paper
• Deep learning of thermodynamic laws from microscopic dynamics.

  2025cites this paper
• Quantum thermal rectification via state-dependent two-photon dissipation

  2025cites this paper
• Surpassing Carnot efficiency with relativistic motion

  2025cites this paper
• Controlling quantum phases with electric fields in one-dimensional Hubbard systems

  2025cites this paper
• Work statistics and quantum trajectories: No-click limit and non-Hermitian Hamiltonians

  2025cites this paper
• Nonequilibrium Thermodynamics of Precision through a Quantum-Centric Computation.

  2025cites this paper
• Non-equilibrium thermodynamics of the quantum Brownian motion: Anomalous non-equilibrium currents arising from complete positivity

  2025cites this paper
• The role of entropy production and thermodynamic uncertainty relations in the asymmetric thermalization of open quantum systems

  2025cites this paper
• Quantum entanglement and extractable work for Gaussian states

  2025cites this paper
• Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect

  2025cites this paper
• Fractal Quantum Thermodynamics and Entropy Scaling Using the McGinty Equation

  2025cites this paper
• Quantum Annealing Algorithms for Estimating Ising Partition Functions

  2025cites this paper
• Landauer principle and thermodynamics of computation

  2025cites this paper
• Experimental demonstration of generalized quantum fluctuation theorems in the presence of coherence

  2025cites this paper
• Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems

  2025cites this paper
• Quantum thermodynamics in a rotating BTZ black hole spacetime

  2025cites this paper
• Coherent heat exchange in a prethermalizing open quantum system

  2025cites this paper
• Fractional Control Gate Protocols for Quantum Engines

  2025cites this paper
• Thermodynamic uncertainty relation for feedback cooling

  2025cites this paper
• Universal Statistics of Charges Exchanges in Non-Abelian Quantum Transport

  2025cites this paper
• Coarse-Grained Quantum Thermodynamics: Observation-Dependent Quantities, Observation-Independent Laws

  2025influential citation
• Fluctuation theorems for multipartite quantum coherence and correlation dynamics

  2025cites this paper
• Fluctuation in energy extraction from quantum batteries: How open should the system be to control it?

  2025cites this paper
• Quantum Coherence and Anomalous Work Extraction in Qubit Gate Dynamics

  2025cites this paper
• Work distribution of quantum fields in static curved spacetimes

  2025cites this paper
• Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems

  2025cites this paper
• AI Work Quantization Model: Closed-System AI Computational Effort Metric

  2025cites this paper
• Entropy production due to spacetime fluctuations

  2024cites this paper
• Fully quantum stochastic entropy production

  2024cites this paper
• Measurement of the work statistics of an open quantum system using a quantum computer

  2024influential citation
• Experimentally probing entropy reduction via iterative quantum information transfer

  2024cites this paper
• Typical positivity of nonequilibrium entropy production for pure states.

  2024cites this paper
• Thermodynamics of a quantum subsystem

  2024cites this paper
• Nanothermodynamics: There’s Plenty of Room on the Inside

  2024cites this paper
• Microscopic theory of spin friction and dissipative spin dynamics

  2024cites this paper
• Energetics and quantumness of Fano coherence generation

  2024cites this paper
• Operational Work Fluctuation Theorem for Open Quantum Systems.

  2024cites this paper
• Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine.

  2024cites this paper
• Dissipative dynamics of an open quantum battery in the BTZ spacetime

  2024cites this paper
• Hierarchical equations of motion for multiple baths (HEOM-MB) and their application to Carnot cycle.

  2024cites this paper
• Quench dynamics in topologically nontrivial quantum many-body systems

  2024cites this paper
• Role of Quantum Coherence in Kinetic Uncertainty Relations.

  2024cites this paper
• Modified Jarzynski equality in a microcanonical ensemble.

  2024cites this paper
• Quantum thermodynamics of open quantum systems: nature of thermal fluctuations

  2024cites this paper
• Quasiprobability distributions with weak measurements

  2024cites this paper
• Classical and quantum thermodynamics in a non-equilibrium regime: Application to thermostatic Stirling engine.

  2024cites this paper
• Emergence of fluctuation relations in UNO

  2024cites this paper
• Quantum thermodynamics of the Caldeira-Leggett model with non-equilibrium Gaussian reservoirs

  2024cites this paper
• Energy exchange statistics and fluctuation theorem for nonthermal asymptotic states.

  2024cites this paper
• Quantum unital Otto heat engines: Using Kirkwood-Dirac quasi-probability for the engine’s coherence to stay alive

  2024cites this paper
• Quantum Uncertainty Relations for Thermodynamic Energy Flows

  2024cites this paper
• Two-stroke thermal machine using spin squeezing operation

  2024cites this paper
• Experimental test of the Crooks fluctuation theorem in a single nuclear spin

  2024cites this paper
• Generalized Quantum Fluctuation Theorem for Energy Exchange.

  2024cites this paper
• Work Sum Rule for Open Quantum Systems.

  2024cites this paper
• Quasiprobabilities in Quantum Thermodynamics and Many-Body Systems

  2024cites this paper
• Quantum computers, quantum computing, and quantum thermodynamics

  2024cites this paper
• Stochastic Thermodynamics at the Quantum-Classical Boundary: A Self-Consistent Framework Based on Adiabatic-Response Theory

  2024cites this paper
• Maxwell's demon across the quantum-to-classical transition

  2024cites this paper
• Classical and quantum thermodynamics described as a system-bath model: The dimensionless minimum work principle.

  2024cites this paper
• Interferometry of quantum correlation functions to access quasiprobability distribution of work

  2024cites this paper
• Work and heat of a quantum system far from its equilibrium state

  2024cites this paper
• Force-current structure in Markovian open quantum systems and its applications: Geometric housekeeping-excess decomposition and thermodynamic trade-off relations

  2024cites this paper
• Quantum speed limit for Kirkwood–Dirac quasiprobabilities

  2024cites this paper
• Quantum heat engine based on quantum interferometry: The SU(1,1) Otto cycle

  2024cites this paper
• Revising the quantum work fluctuation framework to encompass energy conservation

  2024cites this paper
• Probing Quantum Anomalous Heat Flow Using Mid‐Circuit Measurements

  2024cites this paper
• Thermodynamic entropy production in the dynamical Casimir effect

  2023cites this paper
• Quantum non-Markovianity, quantum coherence and extractable work in a general quantum process.

  2023cites this paper
• Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations

  2023cites this paper
• Quantum thermodynamic cycles in the forward and time-reversed regimes

  2023cites this paper
• Thermodynamic perspective on quantum fluctuations

  2023cites this paper
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions

  2023cites this paper
• Work Fluctuations in Ergotropic Heat Engines

  2023cites this paper
• Quantum coherence and the principle of microscopic reversibility

  2023cites this paper
• Quantum Fluctuation Theorem for Arbitrary Measurement and Feedback Schemes.

  2023influential citation
• Work, Heat and Internal Energy in Open Quantum Systems: A Comparison of Four Approaches from the Autonomous System Framework

  2023cites this paper
• Non-Abelian Transport Distinguishes Three Usually Equivalent Notions of Entropy Production

  2023cites this paper
• Universal Defects Statistics with Strong Long-Range Interactions.

  2023cites this paper
• Quantum simulations of time-dependent Hamiltonians beyond the quasistatic approximation

  2023cites this paper
• Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

  2023cites this paper
• Monitored nonadiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants.

  2023cites this paper
• A convenient Keldysh contour for thermodynamically consistent perturbative and semiclassical expansions

  2023cites this paper
• Thermodynamic Geometry of Nonequilibrium Transport in Cyclically Driven Thermal Devices

  2023cites this paper