Equivalent definitions of the quantum nonadiabatic entropy production

Abstract

The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.

arXiv comment13 pages

References in corpus (27)

• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Steady State Thermodynamics of Langevin Systems
• A Straightforward Introduction to Continuous Quantum Measurement
• Three detailed fluctuation theorems
• Fluctuation theorems for stochastic dynamics
• The Three Faces of the Second Law: I. Master Equation Formulation
• A holographic proof of the strong subadditivity of entanglement entropy
• A simple model of quantum trajectories
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• Integral fluctuation theorem for the housekeeping heat
• Monotonicity of quantum relative entropy revisited
• Quantum Trajectory Approach to the Stochastic Thermodynamics of a Forced Harmonic Oscillator
• Entropy production along nonequilibrium quantum jump trajectories
• Quantum Operation Time Reversal
• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• Non-equilibrium thermodynamics of stochastic systems with odd and even variables
• Generators of Detailed Balance Quantum Markov Semigroups
• Quantum Fluctuation Relations for the Lindblad Master Equation
• Geometrical Expression of Excess Entropy Production
• A nonequilibrium extension of the Clausius heat theorem
• Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states
• Equivalence of two Bochkov-Kuzovlev equalities in quantum two-level systems
• Nonequilibrium heat capacity
• Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction
• The Second Law of Steady State Thermodynamics for Nonequilibrium Quantum Dynamics
• Quantum Trajectories in Random Environment: the Statistical Model for a Heat Bath
• Operator equality on entropy production in quantum Markovian master equations

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• Quantum Thermodynamics
• Irreversible entropy production, from quantum to classical
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• Thermodynamic uncertainty relation in slowly driven quantum heat engines
• Periodic Thermodynamics of Open Quantum Systems
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Quantum fluctuations hinder finite-time information erasure near the Landauer limit
• Non-thermal quantum engine in transmon qubits
• Quantum Fluctuation Theorems
• Quantum jump model for a system with a finite-size environment
• Joint statistics of work and entropy production along quantum trajectories
• The production rate of the system-bath mutual information
• Fluctuations of work in nearly adiabatically driven open quantum systems
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• The correlation production in thermodynamics
• Three heats in strongly coupled system and bath
• Testing a Quantum Heat Pump with a Two-Level Spin
• Force-current structure in Markovian open quantum systems and its applications: geometric housekeeping-excess decomposition and thermodynamic trade-off relations
• Information geometry of transitions between quantum nonequilibrium steady states
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Calorimetric measurement of work for a driven harmonic oscillator
• Quantum thermodynamics under continuous monitoring: a general framework
• The correlational entropy production during the local relaxation in a many body system with Ising interactions