Nonequilibrium quantum-impurities: from entropy production to information theory

TL;DR

This paper explores entropy production in nonequilibrium quantum impurity models, revealing its information-theoretic interpretation and demonstrating its positivity in steady states through specific models.

Contribution

It introduces an information-theoretic perspective on entropy production in quantum impurity models driven out of equilibrium, linking thermodynamics with information theory.

Findings

Entropy production is positive in nonequilibrium steady states.

Entropy production can be interpreted via Shannon entropy and Kullback-Leibler divergence.

Application to Resonance Level and Kondo models confirms theoretical insights.

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.