熱力学ポテンシャル
( ∂ U ∂ S − T e x ) δ S + ( ∂ U ∂ V + p e x ) δ V + ( ∂ U ∂ N − μ e x ) δ N = 0 {\displaystyle \left({\frac {\partial U}{\partial S}}-T_{\mathrm {ex} }\right)\delta S+\left({\frac {\partial U}{\partial V}}+p_{\mathrm {ex} }\right)\delta V+\left({\frac {\partial U}{\partial N}}-\mu _{\mathrm {ex} }\right)\delta N=0}
および、2次変分について
1 2 ( ∂ 2 U ∂ S 2 δ S 2 + ∂ 2 U ∂ V 2 δ V 2 + ∂ 2 U ∂ N 2 δ N 2 ) + ∂ 2 U ∂ S ∂ V δ S δ V + ∂ 2 U ∂ S ∂ N δ S δ N + ∂ 2 U ∂ V ∂ N δ V δ N > 0 {\displaystyle {\frac {1}{2}}\left({\frac {\partial ^{2}U}{\partial S^{2}}}\delta S^{2}+{\frac {\partial ^{2}U}{\partial V^{2}}}\delta V^{2}+{\frac {\partial ^{2}U}{\partial N^{2}}}\delta N^{2}\right)+{\frac {\partial ^{2}U}{\partial S\partial V}}\delta S\delta V+{\frac {\partial ^{2}U}{\partial S\partial N}}\delta S\delta N+{\frac {\partial ^{2}U}{\partial V\partial N}}\delta V\delta N>0}