  In this talk I discuss some features of the entanglement entropy for fuzzy
geometry, focusing on its dependence on the background fields and the spin
connection of the emergent continuous manifold in a large $N$ limit. Using the
Landau-Hall paradigm for fuzzy geometry, this is argued to be given by a
generalized Chern-Simons form, making a point of connection with the
thermodynamic view of gravity. Matter-gravity couplings are also considered in
the same framework; they naturally lead to certain specific nonminimal
couplings involving powers of the curvature.
