Quantum limit to the second law by magneto-caloric effect, adiabatic phase transition of mesoscopic-size Type I superconductor particles

Under ideal conditions, a quantum limit to the second law of thermodynamics is predicted for the magneto-caloric effect, adiabatic phase transition of a mesoscopic-size Type I superconductor particle. J. Bardeen proposed the presence of hysteresis in the critical magnetic field that would theoretically negate the requirement of ideal conditions of the subject phase transition. However, A.B. Pippard has shown that hysteresis of the critical magnetic field deviates from the prediction of J. Bardeen, such that the requisite ideal conditions of the subject phase transition are theoretically realizable.