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Maxwell's equal-area law for Gauss-Bonnet Anti-de Sitter black holes

Interpreting the cosmological constant Λas a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we study the Maxwell's equal area law of higher dimensional Gauss-Bonnet-AdS black holes in extended phase space. These black hole solutions critically behave like Van der Waals systems. It has been realized that below the critical temperature T_c the stable equilibrium is violated. We show through calculations that the critical behaviors for the uncharged black holes only appear in d=5. For the charged case, we analyse solutions in d = 5 and d = 6 separately and find that, up to some constrains, the critical behaviors only appear in the spherical topology. Using the Maxwell's construction, we also find the isobar line for which the liquid-gas-like phases coexist.