Nonequilibrium thermodynamics formulation for electric transients. (I). The generalized Drude equation

The application of the nonequilibrium relaxation theory to describe the transient of electric charged system in a material out of equilibrium is presented. We show that in order to generalize the Drude equation, an internal variable has to be introduced to accommodate the influence of a possible internal mechanism, which modifies the natural evolution of a charged system. This variable could represent one of the following effects: (a) Trapped charges, (b) collective behavior of the electric charges with interactions and (c) resonance processes. The final description of the free charge evolution, affected by the internal process in the material, is expressed by means of a second-order differential relation, the so-called generalized Drudeʹs equation. The application of this last result to different physical situations is discussed.