  We study entanglement between the spin components of the
Bardeen-Cooper-Schrieffer (BCS) ground state by calculating the full
entanglement spectrum and the corresponding von Neumann entanglement entropy.
The entanglement spectrum is effectively modeled by a generalized Gibbs
ensemble (GGE) of non-interacting electrons, which may be approximated by a
canonical ensemble at the BCS critical temperature. We further demonstrate that
the entanglement entropy is jointly proportional to the pairing energy and to
the number of electrons about the Fermi surface (an area law). Furthermore, the
entanglement entropy is also proportional to the number fluctuations of either
spin component in the BCS state.
