The Little-Parks effect in an inhomogeneous superconducting ring
  An inhomogeneous superconducting ring placed in a magnetic field is considered. It is shown that the superconducting transition of the section with lowest critical temperature may be a first order phase transition if the magnetic flux contained within the ring is not divisible by the flux quantum. In the visinity of this transition, thermal fluctuations can induce the direct voltage in the ring with rather small sizes. The voltage value depends in a periodic manner on the magnetic flux contained within the ring. According to this result, the entropy value can be decreased in the considered quantum system. The chaotic heat energy can be transformed in the electric energy of the direct current. 
A.V.Nikulov and I.N.Zhilyaev