  The boundary Weyl anomalies live on a codimension-1 boundary, $\partial {\cal
M}$. The entanglement entropy originates from infinite correlations on both
sides of a codimension-2 surface, $\Sigma$. Motivated to have a further
understanding of the boundary effects, we introduce a notion of reduction
entropy, which, guided by thermodynamics, is a combination of the boundary
effective action and the boundary stress tensor defined by allowing the metric
on $\partial {\cal M}$ to fluctuate. We discuss how a reduction might be
performed so that the reduction entropy reproduces the entanglement structure.
