Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization

TL;DR

This paper investigates microscopic contributions to entropy production in a quantum system, revealing that bath deviations from thermality and bath-bath correlations dominate entropy production across all times, even in an integrable model.

Contribution

It provides a detailed numerical analysis of entropy production at microscopic levels in a quantum transport model, highlighting the role of bath correlations and deviations from thermality.

Findings

Entropy production is mainly due to microscopic deviations from thermality.

Bath temperatures and chemical potentials thermalize despite integrability.

Bath-bath correlations are insensitive to system-bath coupling strength.

Abstract

Based on exact integration of the Schr\"odinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes.