  We study the role of the Gauss-Bonnet corrections to the gravity action on
the charged AdS black hole in presence of rank 3 antisymmetric Kalb Ramond
tensor field strength. Analyzing the branch singularity and the killing
horizon, we explicitly derive various thermodynamic parameters and study their
behaviour in presence of five dimensional Gauss-Bonnet coupling in AdS
space-time. The possibility of a second order phase transition is explored in
the light of AdS/CMT correspondence and various critical exponents associated
with the discontinuities of the various thermodynamic parameters are
determined. We further comment on the universality of the well known Rushbrooke
Josephson scaling law and derive a relation between the degree of homogeneity
appearing in various free energies and the critical exponents by homogeneous
hypothesis test. By making use of the constraints appearing from Hawking
temperature and Gauss-Bonnet extended gravity version of Kubo formula we
introduce a bound on the five dimensional Gauss-Bonnet coupling and the
viscosity entropy ratio in the four dimensional holographic Conformal Field
Theory (CFT) dual. This yields a fractional deviation in viscosity entropy
ratio from the result obtained from Einstein gravity.
