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Thermodynamic Equilibrium

Thermodynamic equilibrium is a state where the system's macroscopic properties (temperature, pressure, composition) are constant over time.
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The statement of the theorem

A system is at thermodynamic equilibrium if and only if the total Gibbs Free Energy GG is minimized with respect to changes in state variables (T,P,xT, P, \mathbf{x}), such that the differential change in GG is zero under constant constraints:\ndG=0subject to dT=0,dP=0, and ∑xidN~i=0dG = 0 \quad \text{subject to } dT=0, dP=0, \text{ and } \sum x_i d\tilde{N}_i = 0