  In this work we study the statistical and thermodynamic properties of the
horizon fluid corresponding to the Boulware-Deser (BD) black hole of
Einstein-Gauss-Bonnet (EGB) gravity. Using mean field theory, we show
explicitly that the BD fluid exhibits the coexistence of two phases, a BEC and
a non-condensed phase corresponding to the Einstein term and the Gauss-Bonnet
term in the gravity action, respectively. In the fluid description, the
high-energy corrections associated to Gauss-Bonnet gravity are modeled as
excitations of the fluid medium. We provide statistical modeling of the excited
part of the fluid and explicitly show that it is characterized by a generalized
dispersion relation which in $D=6$ dimensions corresponds to a non-relativistic
fluid. We also shed light on the ambiguity found in the literature regarding
the expression of the entropy of the horizon fluid. We provide a general
prescription to obtain the entropy and show that it is indeed given by Wald
entropy.
