  We consider two-dimensional states of matter satisfying an uniform area law
for entanglement. We show that the topological entanglement entropy is equal to
the minimum relative entropy distance from the reduced state to the set of
thermal states of local models. The argument is based on strong subadditivity
of quantum entropy. For states with zero topological entanglement entropy, in
particular, the formula gives locality of the states at the boundary of a
region as thermal states of local Hamiltonians. It also implies that the
entanglement spectrum of a two-dimensional region is equal to the spectrum of a
one-dimensional local thermal state on the boundary of the region.
