Abstract
The purpose of this paper 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 [Formula: see text] 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 [Formula: see text]. 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, i.e. the pressure. Our result offers direct evidence of no violation of the second law in the extended phase-space.
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