Generalized thermodynamic identity and new Maxwell's law for charged AdS   black hole
  We study the thermodynamic properties of the RN-AdS black hole in full phase space and propose a generalized thermodynamic identity. As an example, we use it to find relations of thermodynamical coefficients between the grand canonical and canonical ensembles. We also show, for the first order phase transition, that the usual Maxwell's equal area law should be extended to a new form for the RN-AdS black hole. 
Zixu Zhao and Jiliang Jing
gr-qc hep-th