On apparent breaking the second law of thermodynamics in quantum   transport studies
  We consider a model for stationary electronic transport through a one-dimensional chain of two leads attached to a perturbed central region (quantum dot) in the regime where the theory proposed recently by Capek for a similar model of phonon transport predicts the striking phenomenon of a permanent current between the leads. This result based on a rigorous but asymptotic Davies theory is at variance with the zero current yielded by direct transport calculations which can be carried out in the present model. We find the permanent current to be within the error of the asymptotic expansion for finite couplings, and identify cancelling terms of the same order. 
Tomas Novotny