Generalized thermodynamic potentials for mesoscopic conductors in the   presence of transport
  It is shown that the nonequilibrium steady-state of a phase-coherent conductor can be described by a generalized thermodynamic potential based on the concept of partial densities of states. This is possible due to the fact that dissipation takes place only in the contacts for the emitted carriers. Long-range Coulomb interaction is included, and charge conservation and gauge invariance are satisfied. The theory is illustrated for a mesoscopic capacitor with leakage. 
Thomas Christen