In thermodynamics, chemical potential, for standard chemical or biological systems, is the change in Gibbs free energy with respect to change in amount of component, with pressure, temperature, and amounts of other components being constant. [1]

Overview
In 1876, American mathematical physicist Willard Gibbs, introduced the concept of chemical potential, symbolized by μ, which he defined as:

“If to any homogeneous mass in a state of hydrostatic stress we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and it entropy and volume remaining unchanged, the increase of the energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered.”

Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a substance, whether capable or not of existing by itself as a homogeneous body. [2]

In 1885, author George Liveing, in developing a thermo-dynamic theory of molecular kinetic energy, defined potential, by stating that “the fundamental notion connected with equality of potential being that when two forms of energy are at the same potential in the same substance there is no tendency for either to be increased at the expense of the other; but that if they are at unequal potentials there is a tendency to an equalization; also that when two bodies have their energies at equal potentials there is no tendency for the energy of one to increase at the expense of the other, while if they are at unequal potentials there is a tendency to equalization by the passage of energy from one body to the other.” [3] This process, from one point of view, is called thermalization in modern terms.

Gibbs, to note, never used the term ‘‘chemical potential’’, but only "potential" and "intrinsic potential", the latter of which he defined as a derivative that is "entirely determined at any point in a mass by the nature and state of the mass about that point."

In 1890s, American
physical chemist Wilder Bancroft, a PhD student of Wilhelm Ostwald, began using the term "chemical potential" in references to Gibbs' conception of potential. [4]

Social potential
See main: Social chemical potential
In 1994, Australian physical chemist John Christie, in his "A Survey of Thermodynamical Ideas", built on the work of John Neumann (1932) and discusses how microcanonical ensembles can be used to formulate economic analogies, wherein he employs a 6-person "island model", in which goods are traded, resulting in a microstate currency distribution; how social equilibrium relates to Gibbs free energy; how coupling and time scales may play a role, etc., in economic processes; then discusses Gibbs free energy, in definitional terms, and alludes to the premise that when an inhabitant enters or leaves the island—if the island were an "open" system—the “component will move into or out of the system to minimize its chemical potential, i.e. it will tend to flow from regions of higher to lower chemical potential.” [5]

In 2007, American electrochemical engineer Libb Thims extrapolated the concept of chemical potential to sociological movement of humans. [6]

Potential
Potential energy
Population potential

References
1. Daintith, John. (2004). Oxford Dictionary of Chemistry, (pg. 125). New York: Oxford University Press.
2. Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.
3. Liveing, G.D. (1886). “On the Measurement of Kinetic Energy on an Absolute Scale”, Proceedings of the Cambridge Philosophical Society (pg. 318), University Press.
4. Baierlein, Ralph. (2000). “The Elusive Chemical Potential”, American Association of Physics Teachers, Oct.
5. Christie, John R. (1994). “A Survey of Thermodynamical Ideas”, in: Economics and Thermodynamics: New Perspectives on Economic Analysis (editors: Peter Burley and John Foster). Kluwer Academic Publishers.
6. Thims, Libb. (2007). Human Chemistry (Volume One) (pg. 106). Morrisville, NC: LuLu.