  Entropy production is a key quantity characterizing nonequilibrium systems.
However, it can often be difficult to compute in practice, as it requires
detailed information about the system and the dynamics it undergoes. This
becomes even more difficult in the quantum domain, and if one is interested in
generic nonequilibrium reservoirs, for which the standard thermal recipes no
longer apply. In this paper, we derive an upper bound for the entropy
production in terms of the entropy flux for a class of systems for which the
flux is given in terms of a system's observable. Since currents are often
easily accessible in this class of systems, this bound should prove useful for
estimating the entropy production in a broad variety of processes. We
illustrate the applicability of the bound by considering a three-level maser
engine and a system interacting with a squeezed bath.
