How does the entropy in BCS superconductor behave?

Question

In low-temperature superconductor the formation of Cooper pairs results with zero resistivity. The transition to the normal state is second-order phase transition. In Ehrenfest classification it means that the entropy is continuous.

Simultaneously the entropy of superconducting state is much lower due to the Cooper pair formation. In critical temperature they suddenly break to normal Fermi liquid. How does it happen that the entropy doesn't exhibit a sudden jump?

Answer 1

The entropy of the superconducting state is caused by the normal electrons, which number density increases with increasing temperature. At $T_c$ all electrons become normal. All that is perfectly explained in the two-fluid model of Gorter and Casimir. Read Shoenberg's book.