Quantum Fluctuation Relations for the Lindblad Master Equation

Abstract

An open quantum system interacting with its environment can be modeled under suitable assumptions as a Markov process, described by a Lindblad master equation. In this work, we derive a general set of fluctuation relations for systems governed by a Lindblad equation. These identities provide quantum versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response regime, these fluctuation relations yield a fluctuation-dissipation theorem (FDT) valid for a stationary state arbitrarily far from equilibrium. For a closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula.

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Cited by in corpus (68)

• Speed Limit for Classical Stochastic Processes
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Entropy production along nonequilibrium quantum jump trajectories
• A non-equilibrium quantum Landauer principle
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• Fully quantum fluctuation theorems
• Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Absorbing state phase transition with competing quantum and classical fluctuations
• Symmetry and the thermodynamics of currents in open quantum systems
• Integral Quantum Fluctuation Theorems under Measurement and Feedback control
• Verification of the Quantum Nonequilibrium Work Relation in the Presence of Decoherence
• Employing Circuit QED to Measure Nonequilibrium Work Fluctuations
• Harnessing symmetry to control quantum transport
• Optimal protocols for slowly-driven quantum processes
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Entropic fluctuations of quantum dynamical semigroups
• Thermodynamic consistency of quantum master equations
• Quantum Trajectory Thermodynamics with Discrete Feedback Control
• Large deviations at level 2.5 for Markovian open quantum systems: quantum jumps and quantum state diffusion
• Non-equilibrium universality in the dynamics of dissipative cold atomic gases
• Quantum nonequilibrium equalities with absolute irreversibility
• Steering heat engines: a truly quantum Maxwell demon
• Characteristic Functions Based on Quantum Jump Trajectory
• Equivalent definitions of the quantum nonadiabatic entropy production
• Fluctuation Theorems for Continuous Quantum Measurement and Absolute Irreversibility
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Quantum jump model for a system with a finite-size environment
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Classifying transport behavior via current fluctuations in open quantum systems
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Response theory for nonequilibrium steady-states of open quantum systems
• Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current
• Fluctuation-dissipation theorem for non-equilibrium quantum systems
• Characterizing a statistical arrow of time in quantum measurement dynamics
• Quasiparticles of Decoherence Processes in Open Quantum Many-Body Systems: Incoherentons
• Kramers' degeneracy for open systems in thermal equilibrium
• Quantum response theory for nonequilibrium steady states
• Time reversals of irreversible quantum maps
• Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State
• Calculating work in weakly driven quantum master equations: backward and forward equations
• Information Fluctuation Theorem for an Open Quantum Bipartite System
• The characteristic functions of quantum heat with baths at different temperatures
• Fluctuations of the heat exchanged between two quantum spin chains
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• A quantum fluctuation theorem for any Lindblad master equation
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• Inferring work by quantum superposing forward and time-reversal evolutions
• Energetic fluctuations in an open quantum process
• Atomic loss and gain as a resource for non-equilibrium phase transitions in optical lattices
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• A perturbative method for nonequilibrium steady state of open quantum systems
• Symmetry-induced fluctuation relations in open quantum systems
• Semi-classical work and quantum work identities in Weyl representation
• Markovian Repeated Interaction Quantum Systems
• Fluctuation Relation for Qubit-Calorimetry
• Nonequilibrium work equalities in isolated quantum systems
• Exploring the extent of validity of quantum work fluctuation theorems in the presence of weak measurements
• Quantum work statistics at strong reservoir coupling
• Lindbladians with multiple steady states: theory and applications
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Calorimetric measurement of work for a driven harmonic oscillator
• Effects from Additional Random Configuration to Linear Response and Modified Fluctuation-Dissipation Relation
• On a tilted Liouville-master equation of open quantum systems
• The EPR Paradox Implies A Minimum Achievable Temperature
• A perspective on Lindblad's Non-Equilibrium Entropy
• Investigation of Dephasing In an Open Quantum System under Chaotic Influence via a Fractional Kohn-Sham Scheme
• Quantum thermodynamics under continuous monitoring: a general framework