The characterization of irreversibility in general quantum processes is an
open problem of increasing techno- logical relevance. Yet, the tools currently
available to this aim are mostly limited to the assessment of dynamics induced
by equilibrium environments, a situation that often does not match the reality
of experiments at the microscopic and mesoscopic scale. We propose a theory of
irreversible entropy production that is suited for quantum systems exposed to
general, non-equilibrium reservoirs. We illustrate our framework by addressing
a set of physically relevant situations that clarify both the features and the
potential of our proposal
