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. Under the reasonable assumption that the magnetic field at the phase boundary is given by the thermodynamic critical field, we show that Joule heating occurs only in the normal region of the material, hence no Joule heating occurs in the superconducting region next to the phase boundary where normal current is expected to flow according to the conventional theory of superconductivity. We discuss the significance of this result.

焦耳热是一种非平衡耗散过程，当电流流过时，会在普通金属中发生，其数量与金属的电阻成正比。当它是由磁通量变化引起的涡流感应时，它也与磁通量变化的速率成正比。在这里，我们表明，在磁场中金属的正常状态和超导状态之间的相变中，焦耳加热的总量由系统的热力学性质决定，并且与正常金属的电阻率无关。在合理假设下，相界处的磁场是由热力学临界场给出的，我们证明焦耳热仅发生在材料的正常区域，因此，根据传统的超导理论，在相边界附近的超导区域中不会发生焦耳热，在该相边界处，正常电流有望流过。我们讨论此结果的重要性。