  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.
