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The velocity field composed of the Berry connection from many-body wavefunctions and electromagnetic vector potential explains the energy-momentumbalance during the reversible superconducting-normal phase transition in thepresence of an externally applied magnetic field. In this formalism, forcesacting on electrons are the Lorentz force and force expressed as the gradientof the kinetic energy. In the stationary situation, they balance; however, aninfinitesimal imbalance of them causes a phase boundary shift. In order toexplain the energy balance during this phase boundary shift, the electromotiveforce of the Faraday's magnetic induction type is considered for the Berryconnection. This theory assumes that supercurrent exists as a collection ofstable quantized loop currents, and the transition from the superconducting tonormal phase is due to the loss of their stabilizations through the thermalfluctuation of the winding numbers of the loop currents. We argue that anabrupt change of loop current states with integral quantum numbers should betreated as a quantum transition; then, the direct conversion of the quantizedloop currents to the magnetic field occurs; consequently, the Joule heatgeneration does not occur during the phase transition.

Reversible superconducting-normal phase transition in a magnetic field:  The energy-momentum balance including the velocity field of the Berry  connection from many-body wave functions