Irreversible Dynamics of Abrikosov Vortices in Type-two Superconductors
  The voltage shift RfIc with respect to the flux flow ohmic behavior of the current-voltage characteristic in type II superconductors is ascribed to the irreversible processes occurring when a vortex crosses defects. We include irreversible effects of the vortices-defects interaction into an effective law of motion. The obtained current-voltage characteristic at finite temperature is in agreement with experimental data. 
S. Pace, G. Filatrella, G.Grimaldi, A. Nigro