  We analyse the entanglement entropy properties of a two-dimensional p-wave
superconductor with Rashba spin-orbit coupling, which displays a rich
phase-space that supports non-trivial topological phases, as the chemical
potential and the Zeeman term are varied. We show that the entanglement entropy
and its derivatives clearly signal the topological transitions and provides a
sensible signature of each topological phase. We separately analyse the
contributions to the entanglement entropy that are proportional to or
independent of the perimeter of the system, as a function of the Hamiltonian
coupling constants and the geometry of the subsystem. We conclude that both
contributions are generically non-universal depending on the specific
Hamiltonian parameters and on the particular geometry. Nevertheless,
contributions to the entanglement entropy due to different kinds of boundaries
or edges simply add up. We also observe a relationship between a topological
contribution to the entanglement entropy in a half- cylinder geometry and the
number of edge states, and that the entanglement spectrum has robust modes
associated with each edge state.
