A recurring theme at the workshop in Dresden last week was quantum impurities driven out of equilibrium. In general this is an extremely difficult problem! One of the approaches discussed was that of Natan Andrei's group, presented here and here. I don't claim to understand the details, but schematically the idea is to remap the general problem into a scattering language. You set up the nonequilibrium aspect (in the case of a quantum dot under bias, this corresponds to setting the chemical potentials of the leads at unequal values) as a boundary condition. By recasting things this way, you can use a clever ansatz to find eigenstates of the scattering form of the problem, and if you're sufficiently clever you can do this for different initial conditions and map out the full nonequilibrium response. Entropy production and eventual relaxation of the charge carriers far from the dot happens "at infinity". Andrei gives a good (if dense) talk, and this formalism seems very promising, though it also seems like actually calculating anything for a realistic system requires really solving for many-body wavefunctions for a given system.