Topological work in nonequilibrium quantum thermodynamics

As a model open quantum system out of equilibrium, we consider a system of electrons coupled to multiple (typically 3) macroscopic electron reservoirs and threaded by an Aharonov-Bohm flux φ. For the noninteracting case, we determine the exact nonequilibrium steady-state density matrix and entropy. We prove that the Nernst theorem (3rd law of thermodynamics) holds without exception for an open quantum system, even for the nonequilibrium case. The general principles are illustrated for the case of a quantum thermocouple. Both the chemical work due to electron exchange between the reservoirs and the topological work due to the Aharonov-Bohm effect must be included in applying the 1st law. The effect of electron-electron interactions on the thermoelectric device performance beyond linear response are investigated.