A dc voltage induced by an external ac current was observed in a system of asymmetric aluminum loops at temperatures corresponding to 0.95–0.98 of the superconducting transition temperature. The voltage magnitude and sign change periodically in a magnetic field with a period corresponding to the magnetic flux quantum through the loop. The amplitude of these oscillations depends nonmonotonically on the amplitude of ac current and is almost independent of its frequency in the range from 100 Hz to 1 MHz. The observed phenomenon is interpreted as the result of displacing the loop into a dynamic resistive state by the external current, where the loop is “switched” back and forth between the closed superconducting state with a nonzero steady current and the nonclosed state with a nonzero resistance along the loop circle. It is shown that voltages are summed up in a system of loops connected in series. For systems with one, three, and twenty loops, the voltage reaches 10, 40, and 300 μ V, respectively.

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.

The law of entropy increase postulates the existence of irreversible processes in physics: the total entropy of an isolated system can increase, but cannot decrease. The annihilation of an electric current in normal metal with the generation of Joule heat because of a non-zero resistance is a well-known example of an irreversible process. The persistent current, an undamped electric current observed in a superconductor, annihilates after the transition into the normal state. Therefore, this transition was considered as an irreversible thermodynamic process before 1933. However, if this transition is irreversible, then the Meissner effect discovered in 1933 is experimental evidence of a process reverse to the irreversible process. Belief in the law of entropy increase forced physicists to change their understanding of the superconducting transition, which is considered a phase transition after 1933. This change has resulted to the internal inconsistency of the conventional theory of superconductivity, which is created within the framework of reversible thermodynamics, but predicts Joule heating. The persistent current annihilates after the transition into the normal state with the generation of Joule heat and reappears during the return to the superconducting state according to this theory and contrary to the law of entropy increase. The success of the conventional theory of superconductivity forces us to consider the validity of belief in the law of entropy increase.

Little-Parks oscillations are observed in a system of 110 series-connected aluminum rings 2 μm in diameter with the use of measuring currents from 10 nA to 1 μA. The measurements show that the amplitude and character of oscillations are independent of the relation between the measuring current and the amplitude of the persistent current. By using asymmetric rings, it is demonstrated that the persistent current has a direction. This means that, in the Little-Parks experiment, the total current in one of the half-rings may be directed against the electric field.

Magnetic field dependences of critical current, resistance, and rectified voltage of asymmetric (half circles of different widths) and symmetrical (half circles of equal widths) aluminum rings close to the super-conducting transition were measured. All these dependences are periodic magnetic field functions with periods corresponding to the flux quantum in the ring. The periodic dependences of critical current measured in opposite directions were found to be close to each other for symmetrical rings and shifted with respect to each other by half the flux quantum in asymmetric rings with ratios between half circle widths of from 1.25 to 2. This shift of the dependences by a quarter of the flux quantum as the ring becomes asymmetric makes critical current anisotropic, which explains the effect of alternating current rectification observed for asymmetric rings. Shifts of the extrema of the periodic dependences of critical current by a quarter of the flux quantum directly contradict the results obtained by measuring asymmetric ring resistance oscillations, whose extrema are, as for symmetrical rings, observed at magnetic fluxes equal to an integer and a half of flux quanta.