Theory of Entropy Production in Quantum Many-Body Systems

Abstract

We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second and third laws of thermodynamics. For weakly-coupled subsystems of an isolated system, an expression for the long time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.

13 pages, revised and expanded as published

References in corpus (13)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum Equivalence and Quantum Signatures in Heat Engines
• Prethermalization and thermalization in models with weak integrability breaking
• Perspective: Quantum Thermodynamics
• Dynamical Correlations after a Quantum Quench
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Robustness of many-body localization in the presence of dissipation
• Microscopic expression for the heat in the adiabatic basis
• Nonequilibrium quantum-impurities: from entropy production to information theory
• Irreversibility and Entropy Production in Transport Phenomena I
• Glass-like Behavior in a System of One Dimensional Fermions after a Quantum Quench
• Nonequilibrium density matrix for simultaneous heat and charge steady-state transport in quantum open systems
• A perturbative method for nonequilibrium steady state of open quantum systems

Cited by in corpus (13)

• Diffusion in generalized hydrodynamics and quasiparticle scattering
• Harnessing symmetry to control quantum transport
• Spin-phase-space-entropy production
• Quantum Fokker-Planck-Kramers equation and entropy production
• DFT-inspired methods for quantum thermodynamics
• Emergent entropy production and hydrodynamics in quantum many-body systems
• Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems
• Boltzmann entropy of a freely expanding quantum ideal gas
• Many-body effects on the thermodynamics of closed quantum systems
• Melting a Hubbard dimer: benchmarks of `ALDA' for quantum thermodynamics
• Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators
• Approximating quantum thermodynamic properties using DFT
• Entropy Production and Thermalization in the One-Atom Maser