In thermal physics entropy S is regarded as a system variable in 1st theorem of thermal dynamics, i.e.
dE(S,V)=TdS-pdV=T(S,V)dS-p(S,V)dV
Entropy is regarded also as thermal potential,i.e.
dS(E,V)=\frac{1}{T(E,V)}dE + \frac{p(E,V)}{T(E,V)}dV
S,V,p,T are usually regarded as variables. My...