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] The concept of chemical potential, symbolized by μ, was introduced in 1876 by American mathematical physicist Willard Gibbs, 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 G.D. 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." That coinage of "chemical potential", however, seems to have been introduced in the 1890s by Cornell physical chemist Wilder Dwight Bancroft, a Ph.D. student of Wilhelm Ostwald, and founder of the Journal of Physical Chemistry. [4]

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,” (pg. 318), Proceedings of the Cambridge Philosophical Society, University Press.
4. Baierlein, Ralph. (2000). “The Elusive Chemical Potential”, American Association of Physics Teachers, Oct.

External links
● Chemical potential – Wikipedia.