Quantum detailed balance conditions and fluctuation relations for thermalizing quantum dynamics

Abstract

Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield the validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples.

9 Pages

References in corpus (26)

• 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
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Path ensembles averages in systems driven far-from-equilibrium
• Quantum Thermodynamics
• Open Quantum Systems. An Introduction
• Quantum Thermodynamics
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Classical and Quantum Fluctuation Theorems for Heat Exchange
• Fluctuation Theorems
• Open Quantum Dynamics: Complete Positivity and Entanglement
• A non-equilibrium quantum Landauer principle
• Quantum Operation Time Reversal
• Fluctuation theorems for quantum processes
• Nonequilibrium potential and fluctuation theorems for quantum maps
• Generators of Detailed Balance Quantum Markov Semigroups
• Correlations in quantum thermodynamics: Heat, work, and entropy production
• Jarzynski equality for quantum stochastic maps
• Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance
• Entropy production and non-Markovian dynamical maps
• Entropic fluctuations of quantum dynamical semigroups
• Time reversals of irreversible quantum maps
• Detailed balance and entanglement
• Fluctuation relation for heat exchange in Markovian open quantum systems

Cited by in corpus (11)

• Geometrical Bounds of the Irreversibility in Markovian Systems
• Experimental test of exchange fluctuation relations in an open quantum system
• Hidden time-reversal symmetry, quantum detailed balance and exact solutions of driven-dissipative quantum systems
• Exact solution of the infinite-range dissipative transverse-field Ising model
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• $C^{\ast }$-fermi systems and detailed balance
• Irreversibility mitigation in unital non-Markovian quantum evolutions
• Symmetry-induced fluctuation relations in open quantum systems
• Stochastic entropy production: Fluctuation relation and irreversibility mitigation in non-unital quantum dynamics
• Operational work fluctuation theorem for open quantum systems
• Energy exchange statistics and fluctuation theorem for non-thermal asymptotic states