The thermodynamic potential minimized at constant temperature and pressure is Gibbs free energy.
Gibbs free energy, commonly written G, is defined as G = H − TS, or equivalently G = U + pV − TS. It combines a system’s enthalpy with its entropy and temperature, making it especially useful for predicting chemical and physical change under constant-temperature, constant-pressure conditions.
At equilibrium, a closed system not driven by an external source such as an applied electrolytic voltage reaches a minimum in Gibbs free energy. A process that can occur spontaneously under these conditions has a negative change in G, while equilibrium corresponds to ΔG = 0. The value of ΔG also sets the maximum non-expansion work available from a reversible process.
Josiah Willard Gibbs developed the concept in the 1870s, initially describing it as “available energy.” The main mix-up is with Helmholtz free energy, A or F, which is minimized at constant temperature and volume. Internal energy and enthalpy are important thermodynamic functions, but they are not the relevant minimum criteria for constant T and p.