 Chemical potential

The chemical potential $\mu =(\partial E/\partial N{)}_{S,V}$ is the energy cost of adding a particle under fixed entropy and volume.

Chemical potential is a fundamental concept in thermodynamics and physical chemistry that describes the change in free energy of a system when an additional amount of substance is introduced, under constant temperature and pressure. It is a measure of the potential energy per particle in a system and reflects how the concentration of a species influences its behavior in a mixture.