Open system dynamics from thermodynamic compatibility

Abstract

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system propagator. Employing spectral analysis we prove the general form of the ensuing master equation. We compare this result to master equations obtained from standard microscopic derivations. The obtained formal structure can be employed to test the compatibility of approximate derivations with thermodynamics. For example, it designates that global master equations are the compatible choice. The axiomatic approach sheds light on the validity of the secular approximation in microscopic derivations, the form of the steady state in heat transport phenomena, and indicates the lack of exceptional points in the dynamics of open quantum systems.

References in corpus (22)

• Thermalization and its mechanism for generic isolated quantum systems
• The numerical renormalization group method for quantum impurity systems
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• Bloch vectors for qudits
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Non-Markovian quantum jumps
• Markovian master equations for quantum thermal machines: local vs global approach
• Markovian Master Equations: A Critical Study
• Adiabatic approximation in open quantum systems
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Performance bound for quantum absorption refrigerators
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Quantum Semi-Markov Processes
• Preservation of Positivity by Dynamical Coarse-Graining
• Staying positive: going beyond Lindblad with perturbative master equations
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Keldysh meets Lindblad: Correlated Gain and Loss in Higher-Order Perturbation Theory
• Dephasing-assisted Gain and Loss in Mesoscopic Quantum Systems
• Quantum Thermodynamics with Degenerate Eigenstate Coherences
• Relaxation, thermalization and Markovian dynamics of two spins coupled to a spin bath