Inherently dissipative normal currents during thermodynamic changes of state in superconductors: Joule heating vs. magnetocaloric cooling

A thermodynamic change of state in the Meissner phase of a superconductor at finite temperature, such as the cooling or the heating it in a constant external magnetic field, inevitably generates normal currents of unpaired electrons. These currents are induced by the time-dependent variations in the local magnetic-flux density associated with the imposed change of state. They may not only lead to certain deviations of the magnetic-field distribution from textbook Meissner profiles, but also cause dissipative Joule heating, which appears to be at odds with the expected reversibility in a truly thermodynamic superconducting state. We show that these normal currents also produce a magnetocaloric cooling, which in total instantaneously and precisely compensates for the dissipated heat, thus ensuring overall energy conservation and reversibility. However, the time-dependent Joule heating and magnetocaloric cooling processes are spatially distinct and therefore must result in small temperature inhomogeneities that will only fade away towards thermodynamic equilibrium after the thermodynamic change of state has halted.