  We demonstrate that the condensed matter quantum systems encompassing two
reservoirs connected by a junction permit a natural definition of flows of
conserved measures, Renyi 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 Renyi 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 posess 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 non-analytical dependence of
the flows on coupling strength in the limit of weak couplings and vanishing
temperatures.
