  In black hole thermodynamics of certain models, the thermodynamic first law
may contain the pressure term. The corresponding entropy follows the area law
whereas the thermodynamic energy is not the same with the black hole mass. If
the pressure can be decomposed into two parts and recombined with the original
thermodynamic quantities, then the thermodynamic energy becomes the black hole
mass and the entropy satisfying the area law turns out to be the corrected
entropy called the Wald entropy, respectively.
