# Potential

In science, potential is a scalar quantity associated with a field. [1] Examples include electrical potential, gravitational potential, chemical potential, in a chemical system sense.

History
In the 18th century, mathematicians, such as Swiss Leonhard Euler, Italian Joseph Lagrange, French Pierre Laplace, brought the logic of infinitesimal calculus to problems in physics, particularly in relation to the application of the concept of “force” to the study of the movement of free particles.

In 1773, Lagrange is credited with having explicitly introduced of the theory of potential into dynamics. Lagrange found that when several planets were clustered, gravitational attraction could be represented by a new coefficient: potential. [8]

The adoption of agreed upon terminology, however, was not immediate. Leonard Euler called the integral of force with respect to distance effort while Lagrange called it potential. [2]

The name “potential function” and fundamental memoir of the subject are due to British mathematical physicist George Green, and his 1828 “An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism”. [3] Green, starting from Laplace’s equation, was the first to define the potential as a function of Cartesian coordinates V(x,y,z), particularly the potential energy of an arbitrary static distribution of electric charges.

The name “potential” was used mathematically in 1840 by German mathematical physicist Carl Gauss (1777-1855). [4]

In 1853, Scottish engineer and physicist William Rankine coined the term “potential energy”.

The distinction between potential and potential function was clarified in 1859 by German physicist Rudolf Clausius. [5]

In 1876, American mathematical physicist Willard Gibbs introduced the concept of “chemical potential” into science. [6]

In 1885, author G.D. Liveing, in loose summary of these views, defined potential, by stating that: [2]

“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.”

The process defined by Liveing, in modern terms, however, is called thermalization.

● Gravitational potential
Thermodynamic potential

References
1. Daintith, John. (2005). Oxford Dictionary of Science. New York: Oxford University Press.
2. Rayner, John, N. (2000). Dynamic Climatology: Basis in Mathematical Physics, (pg. 94). Blackwell Publishing.
3. Green, George. (1828). “An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism.” Nottingham: T. Wheelhouse.
4. Merriman, Mansfield and Woodward, Robert S. (1896). Higher Mathematics: A Textbook for Classical and Engineering Colleges, (pg. 534). J. Wiley & Sons.
5. Clausius, Rudolf. (1859). “The Potential and the Potential Function”, Leipzig: John Ambrose Barth.
6. 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.
7. Liveing, G.D. (1886). “On the Measurement of Kinetic Energy on an Absolute Scale,” (pg. 318), Proceedings of the Cambridge Philosophical Society, University Press.
8. Barnes, Trevor J. and Wilson, Matthew W. (2014). “Big Data, Social Physics, and Spatial Analysis: the Early Years” (note 1, pg. 11) (pre, pdf) (abs) (pdf), Big Data & Society, Apr-Jun:1-14.