Thermal and Electrical Currents in Nanoscale Electronic Interferometers
  We theoretically study thermal transport in an electronic interferometer comprising a parallel circuit of two quantum dots, each of which has a tunable single electronic state which are connected to two leads at different temperature.As a result of quantum interference, the heat current through one of the dots is in the opposite direction to the temperature gradient. An excess heat current flows through the other dot. Although locally, heat flows from cold to hot, globally the second law of thermodynamics is not violated because the entropy production associated with heat transfer through the whole device is still positive. The temperature gradient also induces a circulating electrical current, which makes the interferometer magnetically polarized. 
Sam Young Cho and Ross H. McKenzie