Siacci's theorem

Name	Symbol	Formula	Natural variables
Internal energy	$U$	$\int (TdS-pdV+\sum _i{\mu }_{i}d{N}_i)$	$S,V,\{N_i\}$
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)	$\mathrm{\Omega }$, ${\mathrm{\Phi }}_G$	$U-TS-$$\sum _i$${\mu }_i{N}_i$	$T,V,\{{\mu }_i\}$