Quantum force in a superconductor

In order to account for a contradiction of the Little-Parks experiment with Ohm’s law and other fundamental laws, the thermal fluctuation is considered as a dynamic phenomenon and an extra force, called the quantum force, is introduced. A persistent current can exist at zero voltage and nonzero resistance because of the quantum force induced by the thermal fluctuation. Not only the persistent current but also a persistent voltage (a direct voltage in the equilibrium state) can exist in an inhomogeneous superconducting ring. The directions of the persistent current and the persistent voltage coincide in a ring segment with lower critical temperature and are opposite in other ring segments with higher $T_c.$ Consideration of a superconducting ring interrupted by Josephson junction shows a connection of the quantum force with a real mechanical force.