It is shown that when the thermodynamic fluxes are included as independent
thermodynamic state variables of the generalized entropy density, the const
itutive equations for the conserved state variables and the evolution equat
ions for the nonconserved state variables of elastic type-II superconductor
s can be derived systematically. In particular, the transport equations gen
eralizing the Fourier law for heat transport and the time-dependent Ginzbur
g-Landau equation for the relaxation of superelectron are proposed in this
paper.