A test of "fluctuation theorem" in non-Markovian open quantum systems

Abstract

We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E {\bf73}, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the "detailed balance" condition is well satisfied except in a strongly non-equilibrium transient situation, and hence our generalization of the definition of the "entropy production" is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.

21 pages, 5 figures

References in corpus (7)

• Fluctuation theorems: Work is not an observable
• Entropy production as correlation between system and reservoir
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Fluctuation theorems in driven open quantum systems
• Fluctuation theorems for continuously monitored quantum fluxes
• Quantum work relations and response theory
• Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes

Cited by in corpus (11)

• Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
• Fully quantum fluctuation theorems
• Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem
• Entropy production and information fluctuations along quantum trajectories
• Dynamics and thermodynamics of a central spin immersed in a spin bath
• Fluctuation theorems for non-Markovian quantum processes
• Macroscopically deterministic, Markovian thermalization in finite quantum spin systems
• Stochastic Thermodynamics in a Non-Markovian Dynamical System
• The Minimal Modal Interpretation of Quantum Theory
• Microscopic analysis of the microscopic reversibility in quantum systems
• The distribution of work performed on a NIS junction