グランドポテンシャル

${\displaystyle J=F-\mu N}$

${\displaystyle J(T,V,\mu )=F(T,V,N(T,V,\mu ))-\mu \,N(T,V,\mu )}$

${\displaystyle dJ(T,V,\mu )=-S(T,V,\mu )dT-p(T,V,\mu )dV-N(T,V,\mu )d\mu }$

${\displaystyle S(T,V,\mu )=-\left({\frac {\partial J(T,V,\mu )}{\partial T}}\right)_{V,\mu }}$

${\displaystyle p(T,V,\mu )=-\left({\frac {\partial J(T,V,\mu )}{\partial V}}\right)_{T,\mu }}$

${\displaystyle N(T,V,\mu )=-\left({\frac {\partial J(T,V,\mu )}{\partial \mu }}\right)_{T,V}}$

${\displaystyle J=-pV}$

${\displaystyle J(\beta ,\mu )=-{\frac {1}{\beta }}\ln \Xi (\beta ,\mu )}$