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Joule heating in the normal-superconductor phase transition in a magnetic field

Joule heating is a non-equilibrium dissipative process that occurs in a normal metal when an electric current flows, in an amount proportional to the metal's resistance. When it is induced by eddy currents resulting from a change in magnetic flux, it is also proportional to the rate at which the magnetic flux changes. Here we show that in the phase transformation between normal and superconducting states of a metal in a magnetic field, the total amount of Joule heating is determined by the thermodynamic properties of the system and is independent of the resistivity of the normal metal. We also show that Joule heating only occurs in the normal region of the material. The conventional theory of superconductivity however predicts that Joule heating occurs also in the superconducting region within a London penetration depth of the phase boundary. This implies that there is a problem with the conventional theory of superconductivity.