Nonequilibrium quantum-impurities: from entropy production to information theory

Abstract

Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This letter discusses these issues in the context of quantum impurity models driven out of equilibrium by attaching the impurity to leads at different chemical potentials and temperatures. We start by pointing out that entropy production is often hidden in traditional treatments of quantum-impurity models. We then use simple thermodynamic arguments to define the rate of entropy production. Using the scattering framework recently developed by the authors we show that the rate of entropy production has a simple information theoretic interpretation in terms of the Shannon entropy and Kullback-Leibler divergence of nonequilibrium distribution function. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady-state. We conclude by applying these ideas to the Resonance Level Model and the Kondo model.

5 pages, 1 figure new version with minor clarifications

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• Nonequilibrium entropy production for open quantum systems
• Thermodynamics of precision in quantum non equilibrium steady states
• Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
• Numerical Evaluation of Shot Noise using Real Time Simulations
• Shot noise in the self-dual Interacting Resonant Level Model
• Conductance scaling in Kondo correlated quantum dots: role of level asymmetry and charging energy
• Theory of Entropy Production in Quantum Many-Body Systems
• Imaginary-time formulation of steady-state nonequilibrium in quantum dot models
• Magnetic field dependence of the thermopower of Kondo-correlated quantum dots
• Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment
• Full density matrix dynamics for large quantum systems: Interactions, Decoherence and Inelastic effects
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• Efficiency bounds for nonequilibrium heat engines
• Non-equilibrium Transport in the Anderson model of a biased Quantum Dot: Scattering Bethe Ansatz Phenomenology
• Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution
• Many-body wavefunctions for quantum impurities out of equilibrium. I. The nonequilibrium Kondo model