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Gibbs Free Energy

G = H - TS, where G is Gibbs free energy, H is enthalpy, T is temperature, and S is entropy.
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The statement of the theorem

Let GG be the Gibbs Free Energy, a state function defined for a system in equilibrium at constant pressure PP and temperature TT. The differential change in GG is given by the fundamental thermodynamic relation: dG=VdP−TdSdG = V dP - T dS where VV is the volume, PP is the pressure, and SS is the entropy. Furthermore, GG can be expressed in terms of the enthalpy HH and entropy SS as: G(T,P,N)=H(T,P,N)−TS(T,P,N)G(T, P, N) = H(T, P, N) - T S(T, P, N) The partial derivatives of GG with respect to its natural variables (T,P,N)(T, P, N) define the system's intensive properties: (∂G∂T)P,N=−S\left(\frac{\partial G}{\partial T}\right)_{P, N} = -S (∂G∂P)T,N=V\left(\frac{\partial G}{\partial P}\right)_{T, N} = V (∂G∂N)T,P=μˉ\left(\frac{\partial G}{\partial N}\right)_{T, P} = \bar{\mu} where μˉ\bar{\mu} is the chemical potential.
Source: Wikipedia