Siacci's theorem

Name	Symbol	Formula	Natural variables
Internal energy	$U$	$\int (TdS-pdV+\sum _{i}\mu _{i}dN_{i})$	$S,V,\{N_{i}\}$
Helmholtz free energy	$F$	$U-TS$	$T,V,\{N_{i}\}$
Enthalpy	$H$	$U+pV$	$S,p,\{N_{i}\}$
Gibbs free energy	$G$	$U+pV-TS$	$T,p,\{N_{i}\}$
Landau Potential (Grand potential)	$\Omega$, $\Phi _{G}$	$U-TS-$$\sum _{i}\,$$\mu _{i}N_{i}$	$T,V,\{\mu _{i}\}$