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Based on exact integration of the Schr\"odinger equation, we numericallystudy microscopic contributions to the entropy production for the singleelectron transistor, a paradigmatic model describing a single Fermi leveltunnel coupled to two baths of free fermions. To this end, we decompose theentropy production into a sum of information theoretic terms and study themacross all relevant time scales, including the nonequilibrium steady stateregime and the final stage of global thermalization. We find that the entropyproduction is dominated for most times by microscopic deviations fromthermality in the baths and the correlation between (but not inside) the baths.Despite these microscopic deviations from thermality, the temperatures andchemical potentials of the baths thermalize as expected, even though our modelis integrable. Importantly, this observation is confirmed for both initiallymixed and pure states. We further observe that the bath-bath correlations arequite insensitive to the system-bath coupling strength contrary to intuition.Finally, the system-bath correlation, small in an absolute sense, dominates ina relative sense and displays pure quantum correlations for all studiedparameter regimes.

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