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Gibbs Free Energy

A thermodynamic potential that combines energy and entropy to determine the spontaneity of a process at constant temperature and pressure.
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The statement of the theorem

Let S\mathcal{S} be a thermodynamic system characterized by state variables (T,P,N)(T, P, \mathbf{N}), where TT is temperature, PP is pressure, and N\mathbf{N} is the vector of particle numbers. The Gibbs Free Energy GG is defined as the thermodynamic potential such that its differential change dGdG is given by:\n\ndG=−SdT+VdP+∑iμidNidG = -S dT + V dP + \sum_{i} \mu_{i} dN_{i}\n\nwhere SS is the entropy, VV is the volume, and μi\mu_{i} is the chemical potential of species ii. Furthermore, GG is mathematically related to the internal energy UU via the Legendre transformation:\n\nG(T,P,N)=U(S,V,N)+TS−PVG(T, P, \mathbf{N}) = U(S, V, \mathbf{N}) + T S - P V\n\nFor an infinitesimal process, the criterion for spontaneity is ΔG≤0\Delta G \le 0, with equality holding at equilibrium, which implies that the maximum entropy principle dictates the system evolution along the path minimizing GG for fixed TT and PP.
Source: Wikipedia