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[tex]dE(S,V)=TdS-pdV=T(S,V)dS-p(S,V)dV[/tex]

Entropy is regarded also as thermal potential,i.e.

[tex]dS(E,V)=\frac{1}{T(E,V)}dE + \frac{p(E,V)}{T(E,V)}dV[/tex]

S,V,p,T are usually regarded as variables. My question is that other variables V, p, T can be also treated as thermal potentials ? Can exchanging roles of variable and thermal potential take place only for the pair of E and S ?