  The ground states of topological orders condense extended objects and support
topological excitations. This nontrivial property leads to nonzero topological
entanglement entropy $S_{topo}$ for conventional topological orders. Fracton
topological order is an exotic class of models which is beyond the description
of TQFT. With some assumptions about the condensates and the topological
excitations, we derive a lower bound of the nonlocal entanglement entropy
$S_{nonlocal}$ (a generalization of $S_{topo}$). The lower bound applies to
Abelian stabilizer models including conventional topological orders as well as
type \Rom{1} and type \Rom{2} fracton models, and it could be used to
distinguish them. For fracton models, the lower bound shows that $S_{nonlocal}$
could obtain geometry-dependent values, and $S_{nonlocal}$ is extensive for
certain choices of subsystems, including some choices which always give zero
for TQFT. The stability of the lower bound under local perturbations is
discussed.
