A Comment on the Geometric Entropy and Conical Space
  It has been recently pointed out that a definition of the geometric entropy using the partition function in a conical space does not in general lead to a positive definite quantity. For a scalar field model with a non-minimal coupling we clarify the origin of the anomalous behavior from the viewpoint of the canonical formulation. 
M.Hotta, T.Kato and K.Nagata