Abstract
We demonstrate that the condensed matter quantum systems encompassing two reservoirs connected by a junction permit a natural definition of flows of conserved measures, i.e., R\'enyi entropies. Such flows are similar to the flows of physical conserved quantities such as charge and energy. We develop a perturbation technique that permits efficient computation of R\'enyi entropy flows and analyze second- and fourth-order contributions. Second-order approximation was shown to correspond directly to the transition events in the system and thereby to possess a set of intuitive features. The analysis of fourth-order corrections reveals a more complicated picture: The intuitive relations do not hold anymore, and the corrections exhibit divergencies in low-temperature limit, manifesting an intriguing nonanalytical dependence of the flows on coupling strength in the limit of weak couplings and vanishing temperatures.
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