De Sitter entropy: on-shell versus off-shell

For space-time with a Killing horizon, it is assumed that the generalized entropy satisfies the area law. I will show that instead of interpreting generalized de Sitter entropy as an area law, it can be interpreted as a bulk contribution to the entropy.
The bulk entropy, computed on-shell, i.e., by attributing thermodynamic properties to the vacuum, we compute the entropy as a volume integral, rather than as a contribution from the horizon, varying only the Gibbons-Hawking temperature.
The area law is computed off-shell. Namely, we fix the Gibbons-Hawking temperature and do not fix the period of Euclidean time then we have a manifold with conical singularities on the horizon surface. Since all curvature tensors contain delta-like singularities on the horizon surface, we can expand the Euclidean effective action close to the Gibbons-Hawking temperature and compute the entropy.
As a result both approach gives the same result. Hence, in de Sitter space, there are two ways of thinking about entropy: as a bulk or as a boundary (horizon) contribution.