1enthalpy
$H \coloneqq U + pV$
2Gibbs free energy
$G \coloneqq H - TS$
3Helmholtz free energy
$F \coloneqq U - TS$
4criterion for equilibrium at constant $U$ and $V$ (isolated system)
$dS \ge 0$, or $S_{max}$ composition
5criterion for equilibrium at constant $T$ and $V$ (closed system)
$dF \le 0$, or $F_{min}$ composition
6criterion for equilibrium at constant $T$ and $p$ (closed system)
$dG \le 0$, or $G_{min}$ composition
7chemical potential
$\mu_i = \left( \frac{\partial G}{\partial n_i} \right)_{T, p, n_{j \neq i}}$
8Gibbs free energy in terms of chemical potential
$G = \sum_{i} n_i \mu_i$
9specific heat at constant volume
$c_v \coloneqq \left( \frac{\partial u}{\partial T} \right)_v$
10specific heat at constant pressure
$c_p \coloneqq \left( \frac{\partial h}{\partial T} \right)_p$
11isobaric compressibility
$\alpha \coloneqq \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p$
12isothermal compressibility
$\kappa \coloneqq - \frac{1}{V} \left( \frac{\partial V}{\partial p} \right)_T$
13isentropic compressibility
$\beta \coloneqq - \frac{1}{V} \left( \frac{\partial V}{\partial p} \right)_S$
14for fixed composition, all TD partials can be written in terms of...
$\alpha , \kappa , c_p , p , v , T$