Chemical Potential
The change in system free energy per added particle at constant temperature and pressure.
Governing formula
μ = (∂G / ∂N)_{T,P} = (∂U / ∂N)_{S,V}
SI unit
J/particle (or J/mol)
In depth
Chemical potential governs particle flow: particles diffuse spontaneously from regions of higher chemical potential to lower chemical potential until $μ$ is uniform.
Examples in the real world
Osmotic pressure across semi-permeable cell membranes or phase equilibrium between liquid water and water vapor.