  The purpose of the current letter is to give some relevant clarification on
the validity of the laws of thermodynamics and the stability of the horizon by
scalar field scattering formalism. On the one side, the connection between the
energy of the absorbed particle and the change of the enthalpy of the black
hole appears to resolve the violation of the second law. On the other side,
such connection stipulates a fixed rank of the gauge group $N$ in the boundary
conformal field theory which is against the extended phase space spirit, where
the cosmological constant is allowed to vary inducing a holographical dually
changing of $N$. By recalling the Grand potential, we suggest more stringent
conditions under which the second law holds taking into account the missing
information about the variation of the cosmological constant ie. the pressure.
Our result offers direct evidence of no violation of the second law in the
extended phase space.
