  The recently proposed gravitational entropy generalize the usual black hole
entropy to Euclidean solutions without U(1) symmetry in the framework of
Einstein gravity. The entropy of such smooth configuration is given by the area
of minimal surface, therefore explaining the Ryu-Takayanagi formula of
holographic entanglement entropy. In this note we investigate the generalized
gravitational entropy for general Lovelock gravity in arbitrary dimensions. We
use the replica trick and consider the Euclidean bulk spacetime with conical
singularity localized at a codimension two surface. We obtain a constraint
equation for the surface by requiring the bulk equation of motion to be of good
behavior. When the bulk spacetime is maximally symmetric, the constraints show
that the traces of the extrinsic curvatures of the surface are vanishing, i.e.
the surface has to be geometrically a minimal surface. However the constraint
equation cannot be obtained by the variation of the known functional for
holographic entanglement entropy in Lovelock gravity.
