  We study the entanglement spectra of bilayer quantum Hall systems at total
filling factor nu=1. In the interlayer-coherent phase at layer separations
smaller than a critical value, the entanglement spectra show a striking
similarity to the energy spectra of the corresponding monolayer systems around
half filling. The transition to the incoherent phase can be followed in terms
of low-lying entanglement levels. Finally, we describe the connection between
those two types of spectra in terms of an effective temperature leading to
relations for the entanglement entropy which are in full analogy to canonical
thermodynamics.
