A basic thermodynamic problem in the dynamic interaction between vortices and defects

We show that in the strong pinning case, when the interaction among vortices can be neglected, the usual analysis of pinning centers based on the near equilibrium free energy cannot fully reproduce the usually observed voltage behavior. The experimental current-voltage characteristics indicate the presence of additional energy losses in the dynamic interaction between vortices and defects, which we ascribe to the non-equilibrium phenomena occurring when vortices cross defects. In order to take into account these relaxation phenomena, we introduce a velocity-dependent pinning force, which also in the case of isolated vortices in the strong pinning limit, reproduces for I > Ic a voltage shift, as in the experimental curves.