  We demonstrate, in an elementary manner, that given a partition of the single
particle Hilbert space into orthogonal subspaces, a Fermi sea may be factored
into pairs of entangled modes, similar to a BCS state. We derive expressions
for the entropy and for the particle number fluctuations of a subspace of a
fermi sea, at zero and finite temperatures, and relate these by a lower bound
on the entropy. As an application we investigate analytically and numerically
these quantities for electrons in the lowest Landau level of a quantum Hall
sample.
