# Josiah Willard Gibbs

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## Gibbs, Josiah Willard

**Gibbs, Josiah Willard,**1839–1903, American mathematical physicist, b. New Haven, Conn., grad. Yale, 1858. He studied abroad and was professor of mathematical physics at Yale from 1871. His great contributions to physical chemistry and thermodynamics have had a profound effect on industry, notably in the production of ammonia. He formulated the concept of chemical potential. In mathematics he wrote on quaternions and was influential in developing vector analysis. His work in statistical mechanics was especially important. Gibbs also contributed to crystallography, the determination of planetary and comet orbits, and electromagnetic theory. James Clerk Maxwell was one of the first European scientists to recognize Gibbs as a theoretical physicist of international stature. Gibbs was also interested in the practical side of science; his doctorate was the first granted by Yale for an engineering thesis, and he received a patent (1866) for an improved type of railroad brake. His

*Scientific Papers*appeared in 1906 (repr. 1961) and his

*Collected Works*in 1928.

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.

## Gibbs, Josiah Willard

Born Feb. 11, 1839, in New Haven; died there Apr. 28, 1903. American theoretical physicist. One of the founders of thermodynamics and statistical mechanics.

Gibbs graduated from Yale University in 1858. In 1863 he received the degree of doctor of philosophy from Yale University, and in 1871 he was appointed a professor there. He systematized thermodynamics and statistical mechanics, completing their theoretical formulation. Already in his first articles Gibbs developed graphic methods of investigating thermodynamic systems, introduced three-dimensional diagrams, and obtained the correlation between volume, energy, and entropy of matter. In the treatise *On the Equilibrium of Heterogeneous Substances*, which he wrote between 1874 and 1878, Gibbs developed the theory of thermodynamic potentials, proved the phase rule (the general condition of equilibrium of heterogeneous systems), and created the thermodynamics of surface phenomena and electrochemical processes. He generalized the principle of entropy, applying the second law of thermodynamics to a broad range of processes, and derived the fundamental equations that permit the determination of the direction of reactions and conditions of equilibrium for a mixture of any complexity. The theory of heterogeneous equilibrium, one of Gibbs’ most abstract theoretical contributions to science, found wide practical application.

His work *Elementary Principles in Statistical Mechanics* was published in 1902. It was the crowning achievement of classical statistical physics, the foundations of which were laid in the works of J. C. Maxwell and L. Boltzmann. The statistical method of research, developed by Gibbs, allows us to ascertain the thermodynamic functions that characterize the state of matter. Gibbs advanced a general theory for the fluctuation in the magnitude of these functions from their equilibrium values, which are determined by formal thermodynamics, and gave an adequate description of the irreversibility of physical phenomena. Gibbs was also one of the creators of vector calculus in its contemporary form *(Elements of Vector Analysis*, 1881-84).

Gibbs displayed a remarkably precise logic in his works and a thoroughness in refining results. To this day, not one error has been found in Gibbs’ works, and all of his ideas remain part of contemporary science.

### WORKS

*The Collected Works*, vols. 1-2. New York-London, 1928.

*The Scientific Papers*, vols. 1-2. New York, 1906.

*In Russian translation:*

*Osnovnye printsipy statisticheskoi mekhaniki*. Moscow-Leningrad, 1946.

*Termodinamicheskie raboty*. Moscow, 1950.

### REFERENCES

Semenchenko, V. K. “D. V. Gibbs i ego osnovnye raboty po termodinamike i statisticheskoi mekhanike (K 50-letiiu so dnia smerti).”*Uspekhi khimii*, 1953, vol. 22, issue 10.

Frankfurt, U. I., and A. M. Frenk.

*Dzhozaiia Villard Gibbs*. Moscow, 1964.

O. V. KUZNETSOVA