In thermodynamics, Josiah Willard Gibbs (1839-1903) is considered as the preeminent thermodynamicist, through the publication of his 1876 On the Equilibrium of Heterogeneous Substances in which, along with German physicist Hermann von Helmhotlz, he is considered as the founder of chemical thermodynamics. [1] His grouped publications in thermodynamics are often referred to as "Gibbsian thermodynamics"; whereas, his 1876 Equilibrium treatise, specifically, has been famously called the Principia of thermodynamics. In commentary on his Equilibrium paper, written over a period of three years, 1875-78, Gibbs stated that: [7]

“I had no sense of the value of time, of my own or others, when I wrote it.”

Through his 1901 work on the statistical mechanic nature of thermodynamics he is considered as one of the central developers of the science of statistical thermodynamics. [2] Gibbs is also referred to as the “father of chemical thermodynamics”. [15] This quote above by Gibbs, to note, might be representative of Csíkszentmihályi flow, a state of timeless associated with frictionless highly productive work output.

Students
The few known direct students of Gibbs include: physicist Henry Bumstead (reviewer for Henry Adams) and mathematician Edwin Wilson (advisor of Paul Samuelson).

Difficulty

See also: Hidden treasures

It might aptly be said that Gibbs' 1876 Equilibrium treatise is the most-difficult-to-read work in all of science. This evidenced, firstly, by the fact that of the supposed 300-scientists that Gibbs mailed his treatise out to, only Maxwell was able to understand it and thereby after so intrigued by it as to spend an entire winter building a three-dimensional plaster surface of Gibbs coordinates. Other noted quotes on the so-called "difficulty" of Gibbs' work are as follows:

“Your Equilibrium is too difficult and too condensed for most, I might say all, readers.”

– John Strutt (Lord Rayleigh), "Letter to Gibbs" (1892)

“It was a number of years before its value was generally known; this delay was due largely to the fact that its mathematical form and rigorous deductive processes make it difficulty reading for anyone, and especially so for students of experimental chemistry whom it concerns most.”

– Henry Bumstead, “Josiah Willard Gibbs”, American Journal of Science (1903)

“The works of Willard Gibbs can only be attacked with profit by the expert mathematician.”

– William Bayliss, Principles of General Physiology (1915)

“Although Gibbs’ treatment of thermodynamics has been accessible in English, French, and German for many years, its highly condensed and abstract form has repulsed the great majority of students, with the result that the science of thermodynamics has been recast in many different moulds during the last fifty years.”

– Frededrick Donnan, Irish physical chemist (1932)

“The original source is, of course, Gibbs, but his discussion is difficult reading.”

– Edward Guggenheim, Modern Thermodynamics by the Methods of Willard Gibb (1933)

“Reading Gibbs' Equilibrium is something like reading Laplace, who frequently omits but the conclusion, with the optimistic remark ‘it is easy to see’, shorthand for things ‘seen’ following hours—sometimes days—of hard work.”

– E.T. Bell, Scottish mathematician (c.1940)

“There is a considerable testimony from eminent men that they found the Equilibrium of Heterogeneous Substances very difficult reading. But that it is obscure or lacking in clarity of style is untrue. It is logical, terse, and requires unrelieved concentration of thought.”

– Lynde Wheeler, Josiah Willard Gibbs: the History of a Great Mind (1951)

“Very few experts in thermodynamics have the ability to read this from cover-to-cover.”

– David Bottomley, Japanese physicist (1999)

“Gibbs’ thermodynamic papers—difficult, abstract, and buried in an obscure journal on the fringes of European scientific awareness-remained for a time virtually unknown except among a small circle of admirers. Fortunately, the latter included physicist James Maxwell, who advocated effectively for Gibbs’ insights and methods. Major centers of Gibbsian influence began to appear in Germany, Holland, and elsewhere, as Nobel Prizing winning careers were launched from a passing remark or footnote in Gibbs’ monumental masterpiece.”

– Frank Weinhold, Classical and Geometrical Theory of Chemical and Phase Thermodynamics (2009)

“The intrepid reader who takes on Gibbs’ Equilibrium can expect months of ‘blind work’.”

– William Cropper, Greatest Physicists (2001)

“Gibbs’ work is much deeper than I ever possibly imagined.”

– Jeff Tuhtan, PhD “A Modeling Approach for Alpine Rivers Impacted by Hydropeaking Including the Second Law Inequality” (2011)

“Gibbs is not an easy read. He wrote in a terse, abstract style and provided few examples to illustrate his general conclusions. In addition, he would seldom tell his readers about the specific problems that led to the work on which he was reporting, much less inform them of any larger project he thought results might further.”

– Robert Deltete, “Josiah Willard Gibbs” (2011) [25]

2005 commemorative Gibbs stamp, showing an overlay of one of Scottish physisict James Maxwell's 1875 thermodynamic surfaces, based on Gibbs' two 1873 graphical thermodynamics papers.

Graphical thermodynamics
In Gibbs’ second graphical paper of 1873, it is said that he extended his graphical methods to three-dimensional space, the first example of which was the volume-pressure-temperature diagram employed by Scottish engineer James Thomson in 1871. [22]

Equilibrium of Heterogeneous Substances
Gibbs is best-known for his 1876, 700-equation Equilibrium treatise on the extrapolation of the thermodynamics of Rudolf Clausius to chemical systems, among others.

The central thread of Gibbs logic, supposedly, employs the variation principle of Joseph Lagrange. [18] More research needs to be done on this topic, however, as Gibbs does not cite Lagrange (nor William Hamilton), but rather bases his work on Clausius; Clausius, in turn, does cite Hamilton, but his derivation seems to be self-standing.

Human thermodynamics
In human thermodynamics, through his theories on the free energy of chemical substances and spontaneity, in relation to human chemical reaction prediction, Gibbs is considered one of central founders. [3] In particular, the most-dominant thermodynamic quantity in chemistry is the the Gibbs free energy, G, named in honor of Gibbs by English physicist Edward Guggenheim in 1933: [19]

Opening preface section to American electrochemical engineer Libb Thims' 2007 textbook Human Chemistry crediting the the development of the entire field of human chemistry, Goethe aside, largely to the work of Gibbs. [3]

The following 2009 summary by American physical chemist Thomas Wallace outlines the role of Gibbs free energy in the process of society: [20]

“The thermodynamic parameters enthalpy H and entropy S represent the variables of heat content and probability, respectively, for the physical, chemical, and biological processes of nature and society. The thermodynamic parameter free energy G represents the fundamental driving force in nature and determines whether physical and chemical processes conducted by nature and society will take place.”

In very simple terms, as explained by German polymath Johann Goethe in 1809, the entire process and workings of society can be described as the summation of all human chemical reactions occurring in the boundary of the society, whereby each individual reaction can be quantified as an elective affinity reaction, wherein the chemical affinity A or force of reaction, shown to be equal to the negative of the change in the free energy by German physicist Hermann Helmholtz in 1882, determines what will occur:

Therefore, the affinities between people, are functions of Gibbs free energy changes involved in human interactions. This description, however, is compounded by the 1941 discovery, by Fritz Lipmann, that free energy coupling occurs.

The Gibbs medal in honor of Gibbs who in 1950 was elected to the Hall of Fame for Great Americans, at New York University. [8] A similar award is the Willard Gibbs Medal a yearly award of the American Chemical Society, founded in 1910 by William A. Converse.

Statistical mechanics
In 1892, Gibbs wrote English physicist John Strutt with characteristic modesty: [13]

“Just now I am trying to get ready for publication something on thermodynamics from the a priori point of view, or rather on 'statistical mechanics' . . . I do not know that I shall have anything particularly new in substance, but shall be contented if I can so choose my standpoint (as seems to me possible) as to get a simpler view of the subject.”

Supposedly, by the term a priori Gibbs meant related to or derived by reasoning from self-evident propositions. In any event, ten years later this work resulted in a classic book, Elementary Principles in Statistical Mechanics (1902), which has since been called the "bible of statistical physics", which put statistical mechanics on a new and more general basis. The influence of Gibbs in this field was staggering, as can be discerned by German physicist Werner Heisenberg's 1973 retrospect commentary: [24]

“When I entered Niels Bohr’s institute in Copenhagen in 1924, the first thing Bohr demanded was that I should read the book of Gibbs on thermodynamics. And he added that Gibbs had been the only physicist who really understood statistical thermodynamics.”

As far as terminology goes, the terms: "statistical mechanics" (coined by Maxwell in 1878), "statistical physics", and "statistical thermodynamics", all essentially address the same subject, the use of statistics to explain thermodynamic laws and behaviors of physical systems, although each seems to have a peculiar flavor and direction of presentation. [14]

German-born American physicist Albert Einstein, unaware of Gibbs’ work, had undertaken a similar generalization of Boltzmann’s theory in theory papers of 1902-1904, but as he later observed: [26]

“I only wish to add that the road taken by Gibbs in his book [Elementary Principles in Statistical Mechanics], which consists in one’s starting directly from the canonical ensemble, is in my opinion preferable to the road I took. Had I been familiar with Gibbs’ book at that time, I would not have published all those papers at all, but would have limited myself to the discussion of just a few points.”

A younger Willard Gibbs in circa 1869. [16]

Education
Gibbs entered Yale University at the age of 15 graduating, in 1858, at the age of 18. [7] He then entered the new Yale graduate school earning the first PhD in engineering in the United States, completed in 1863. Gibbs' PhD thesis was “On the Form of the Teeth of Wheels in Spur Gearing”. [10] In 1871, two years after returning from a study abroad at various universities in Europe, Gibbs became Yale's first professor of mathematical physics.

Tributes
All-in-all, along with German physicist Rudolf Clausius, upon which Gibbs built his rigorous theory, Gibbs is considered, in the words of American Nobel Prize winning chemist John Fenn, "the greatest thermodynamicist of them all". [4] Austrian physicist Ludwig Boltzmann considered Gibbs "the greatest synthetic philosopher since Newton", Einsten judged him "one of the most important and creative minds in the field of science America has produced", and Henry Adams defined him as the "greatest of Americans, judged by his rank in science." [5] American political thermodynamicist Richard Hughes stated that Gibbs "is perhaps the greatest American scientist, ever." [6] The clearest tribute comes from German chemist Wilhelm Ostwald who in 1891:

“The translation of your main work is nearly complete and I cannot resist repeating here my amazement. If you had published this work over a longer period of time in separate essays in an accessible journal, you would now be regarded as by far the greatest thermodynamicist since Clausius—not only in the small circle of those conversant with your work, but universally—and as one who frequently goes far beyond him in the certainty and scope of your physical judgment. The German translation, hopefully, will more secure for it the general recognition it deserves.”

Ostwald spent an entire year translating Gibbs' Equilibrium, this comment made in a letter to Gibbs. [17]

In 1931, American educational theorist Albert Nock gave the following summary about about Gibbs, in the context of eminence: [23]

“In the last generation, this country produced one of the most eminent men of science in the whole world. His name was quite unknown among us while he lived, and it is still unknown. Yet I may say without too great exaggeration that when I heard it mentioned in a professional assembly in the Netherlands two years ago, everybody got down under the table and touched their foreheads to the floor. His name was Josiah Willard Gibbs.”

The "professional assembly", Nock refers to here, may likely have been some convention or meeting of sorts associated with the Dutch school of thermodynamics, although this is only a reasoned guess.

Anecdotes

See main: Thermodynamics anecdotes

Maxwell: During a visit to Cambridge University, in the years circa 1873-78, the president of Yale (likely Reverend Noah Porter, president from 1871 to 1886) inquired about possible people to promote at Yale. [21] The famous Scottish physicist, James Maxwell immediately suggested Gibbs. At this time there was also a socially rather prominent individual, named Alan Gibbs, at Yale. Thus, the president replied with pleasure. "Oh, you mean Alan Gibbs." "No! No!" answered Maxwell; "Willard Gibbs." The president's reply was: [11]


J.J. Thomson: Gibbs had a mailing list of over 300 of the world’s greatest scientists, to which, it has been said, he sent his publications to. Of the bunch, it was Scottish physicist James Maxwell who first took appreciation of Gibbs’ work and began to promote it. One of Gibbs’ biographers, J. G. Crowther, remarked that Maxwell became, in effect, Gibbs’ “intellectual publicity agent”. In the years after Maxwell’s premature death, in 1879, a humorous incident occurred between one of Maxwell’s successors at Cambridge English physicist J.J. Thomson, the discoverer of the electron, and a president of a newly formed American university on a faculty-recruiting mission. As the story went, according to Thomson: [7]

A wall statue of American engineer Willard Gibbs (at Yale University), captioned as "discoverer and interpreter of the laws of chemical equilibrium", the central founder in the history of chemical thermodynamics.

“He came to Cambridge, and asked me if I could tell him of anyone who could make a good Professor of Molecular Physics.” Thomson told him that one of the greatest molecular physicists in the world was Willard Gibbs, and he lived in America. The president responded that Thomson probably meant Wolcott Gibbs, a Harvard chemist. Thomson was empathetic that he did mean Willard Gibbs, and tried to convince his visitor that Gibbs was indeed a great scientist. “He sat thinking for a minute or two”, Thomson continues, “and then said, “I’d like you to give me another name. Willard Gibbs can’t be a man of much personal magnetism or I should have heard of him’.”

Gibbs: Gibbs was not talkative and not prone to giving public speeches. Once at the faculty meeting, however, after long wrangling - whether the curriculum should be expanded to make more space for language classes (thus cutting down on time given to mathematics), or whether math should be taught to all freshmen instead - Gibbs stood up and defensively said:

“Mathematics is a language!”

after which he sat down and did not say a word more thereafter. [12]

Quotes
The following are quotes by Gibbs:

“A mathematician may say anything he pleases—but a physicist must be a least partially sane.”

References
1. (a) Gibbs, J. Willard. (1873). "Graphical Methods in the Thermodynamics of Fluids", Transactions of the Connecticut Academy, I. pp. 309-342, April-May.
4. Fenn, John, B. (1982). Engines, Energy, and Entropy, (pg. v). San Francisco: W.H. Freeman and Co.
5. Staff writer. (1943). “Scientists’ Scientist”, Time, Monday, Jan 04.
6. (a) Richard D. Hughes – California State University, Sacramento.
(b) A Thermodynamic View of Politics (PDF) – by Richard D. Hughes.
7. Cropper, William H. (2004). Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking, (section II: Thermodynamics, pgs. 41-134; ch. 9: “The Greatest Simplicity: Willard Gibbs”, pgs 106-23). Oxford University Press.
8. (a) Johnson, Wayne D. (2004). “Hall of Fame at New York University Medal Series”, MedalCollectors.org.
(b) Issue date: 1964; Sculptor: Stanley Martineau.
9. The Willard Gibbs Award – American Chemical Society.
10. Gibbs, Willard. (1863). “On the Form of the Teeth of Wheels in Spur Gearing” in Gibbs, W. and Wheeler, Lynde P. (1947). The Early Work of Willard Gibbs in Applied Mechanics. Schuman.
11. Capri, Anton Z. (2007). Quips, Quotes, and Quanta (ch. 1: Thermodynamics: Founders and Flounderers, pgs. 1-10) [PDF]. World Scientific.
12. (a) Wheeler, Lynde, P. (1951). Josiah Willard Gibbs - the History of a Great Mind (pg. 173). Woodbridge, Connecticut: Ox Bow Press.
(b) J.W. Gibbs gives a speech (mathematics quotes) – Cut-the-Knot.org.
(c) Other version: Gibbs was known in Yale as a faculty member who never spoke at the meetings. Once, during a discussion another professor argued that students are better of learning another foreign language instead of taking mathematics classes. Gibbs spoke first time. He said, "Mathematics is a language". (Source: Paul Samuelson's "on being an economist".)
13. Josiah Willard Gibbs (1829-1903) – AIP.org.
14. Ebeling, Werner and Sokolov, Igor M. (2005). Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems (ch. 1.2: On history of fundamentals of statistical thermodynamics, pgs. 3-12). World Scientific.
15. Bergethon, Peter R. (1998). The Physical Basis of Biochemistry: the Foundations of Molecular Biophysics (pg. 229). Springer.
16. Josiah Willard Gibbs – MSU Gallery of Chemists.
17. Deltete, Robert J. (1995). “Gibbs and the Energeticists” (pgs. 135-170), in: No Truth Except in the Details: Essays in honor of Martin J. Klein (quote, pg. 149), by Martin J. Klein, Anne J. Kox, Daniel M Siegel. Springer.
18. Comments of Georgi Gladyshev to Libb Thims, during a Chicago visit (12/17/2007).
19. Guggenheim, Edward, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs (pg. 11). London: Methuen & Co.
20. Wallace, Thomas P. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations from Ancient Greece to America (Appendix A: The Fundamentals of Thermodynamics Applied to Society, pgs. 469-89.). AuthorHouse.
21. Presidents of Yale – Yale University.
22. (a) Thomson, James. (1871). “Article”, Proc. Roy. Soc. Lond., XX: 1.
(b) Garrison, Fielding H. (1909). “Josiah Willard Gibbs and his Relation to Modern Science” (pg. 280), Popular Science, 74(27): 470-84.
(c) Garrison, Fielding H. (1909). “Josiah Willard Gibbs and his Relation to Modern Science II”, Popular Science Monthly (van’t Hoff school, pg. 560), Jun 74:551-61.
23. Nock, Albert J. (1932). The Theory of Education in the United States (pg. 104). Ludwig von Mises Institute.
24. Heisenberg, Werner. (1973). “Tradition in Science”, Smithsonian Institution, Lecture, Apr, 24.
25. Deltete, Robert J. (2011). “Josiah Willard Gibbs (1839-1903)”, in: Philosophy of Chemistry (pgs. 89-95, etc.), eds. Dov M. Gabbay, Paul Thagard, John Woods, Robin Findlay Hendry, Andrea Woody, Paul Needham. Elsevier.
26. Weinhold, Frank. (2009). Classical and Geometrical Theory of Chemical and Phase Thermodynamics (pg. 151). Wiley-Interscience.

Further reading
● Hastings, Charles S. (1909). Biographical Memoir of Josiah Willard Gibbs, 1839-1903. National Academy of Sciences.
● Donnan, Frederick G., Haas, Arthur. (1936). A Commentary on the Scientific Writings of J. Willard Gibbs. Yale University Press.
● Rukeyser, Muriel. (1942). Willard Gibbs - American Genius. Garden City, New York: Doubleday, Doran & Co., Inc.
● Wheeler, Lynde, P. (1951). Josiah Willard Gibbs - the History of a Great Mind. Woodbridge, Connecticut: Ox Bow Press.
● Seeger, Raymond J. (1974). Men of physics: J. Willard Gibbs, American mathematical physicist par excellence. Pergamon Press.
● Aris, Rutherford, David, Howard T, and Stuewer, Roger H. (1983). Springs of Scientific Creativity: Essays on the Founders of Modern Science (ch. 5: The Scientific Style of Josiah Willard Gibbs, pgs. 142-62; esp. pg. 150). University of Minnesota Press.
● Reingold, Nathan. (1985). Science in Nineteenth-Century America: A Documented History (section: J. Willard Gibbs, pgs 315-22). University of Chicago Press.
● Klein, Martin J. (1989). “The Scientific Style of Josiah Willard Gibbs”, in: A Century of Mathematics in America, Vol 11., edited by P.M. Harman. Cambridge University Press.
● Caldi, D. G. and Mostow, George D. (1989). Proceedings of the Gibbs Symposium, May 15-17, (section: Gibbs in economics, by Paul Samuelson, pgs. 255-68). American Mathematical Society.

External links
● Josiah Willard Gibbs – Wikipedia.
● Josiah Willard Gibbs Lectures (est. 1923) - American Mathematical Society.
● Gibbs Society of Biological Thermodynamics - University of Virginia.
● Suo, Zhigang. (2007). “Josiah Willard Gibbs and his Two Shorter Papers on Thermodynamics”, iMechanica.org blog, Jan, 06.