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For a thermodynamic system with multiple pairs of intensive/extensivevariables and the thermodynamical coefficients attain finite or infinite valueson the phase boundary, we obtain the two classes of Ehrenfest equations in thefull phase space, and find that the rank of the matrix for these equations cantell us the dimensions of the phase boundary. We also apply this treatment tothe RN-AdS black hole.

Ehrenfest scheme for complex thermodynamic systems in full phase space