On the thermodynamic potentials for superconductors of second type

Within the framework of the Ginzburg - Landau theory, a study is conducted of the local equilibrium expressions for the free energy and Gibbs potential of a superconductor of the second kind (arbitrarily shaped) in an external field and carrying a transport current. It is shown how the London magnetic field $H_L$ and the intrinsic field $H_V$ of vortex filaments may be determined in this general case. Terms isolated from expressions for the thermodynamic potentials are proportional to the circulation sums $H_V$(in the case of free energy) or $H_V$ + + $2H_L$ (in the case of the Gibbs potential) along closed circuits that bound sections connecting the axial lines of the vortex filaments to the superconductor surface. If $H_V$,$H_L$≪$H_{c2}$, these terms yield the basic (dependent on the configuration of the vortex filaments) contribution to the thermodynamic potentials.