A quantum fluctuation theorem for any Lindblad master equation

Abstract

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.

arXiv commentAccepted version

References in corpus (44)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• 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
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Fluctuation theorem for stochastic dynamics
• Path ensembles averages in systems driven far-from-equilibrium
• Three detailed fluctuation theorems
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Nonequilibrium Markov processes conditioned on large deviations
• Thermodynamics of Quantum Jump Trajectories
• Quantum simulation of open-system dynamical maps with trapped ions
• The role of quantum measurement in stochastic thermodynamics
• 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
• Entropy fluctuation theorems in driven open systems: application to electron counting statistics
• Quantum Operation Time Reversal
• Fully quantum fluctuation theorems
• Quantum fluctuation theorems for arbitrary environments: adiabatic and non-adiabatic entropy production
• Fluctuation theorems for quantum processes
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Local detailed balance
• Making rare events typical in Markovian open quantum systems
• Quantum fluctuation theorems beyond two-point measurements
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Thermodynamics of Gambling Demons
• Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
• Quantum thermodynamically consistent local master equations
• Fluctuation Theorems for a Quantum Channel
• Entropy production and information fluctuations along quantum trajectories
• Fluctuations of Quantum Currents and Unravelings of Master Equations
• Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks
• Heat flow in chains driven by thermal noise
• Characteristic Functions Based on Quantum Jump Trajectory
• Quantum Martingale Theory and Entropy Production
• Probing quantum fluctuation theorems in engineered reservoirs
• The distribution function of entropy flow in stochastic systems
• Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis
• A short story of quantum and information thermodynamics

Cited by in corpus (10)

• Quantum thermodynamics of boundary time-crystals
• Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy
• Energy conservation and fluctuation theorem are incompatible for quantum work
• Synchronization-induced violation of thermodynamic uncertainty relations
• Nonreciprocal heat flux via synthetic fields in linear quantum systems
• Thermodynamics of coupled time crystals with an application to energy storage
• Entanglement signature in quantum work statistics in the slow-driving regime
• Fluctuation theorem for time-averaged work
• Single energy measurement Integral Fluctuation theorem and non-projective measurements
• Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems