Lars Onsager

Lars Onsager

Born| (1903-11-27)November 27, 1903

Kristiania (Oslo), Norway

Died| October 5, 1976(1976-10-05) (aged 72)

Coral Gables, Florida, U.S.

Nationality| American
Alma mater|

* Yale University
* Norwegian University of Science and Technology

Known for|

* Quantum vortex
* Negative temperature
* Onsager–Machlup function
* Onsager reaction field
* Onsager hard rod model
* Onsager regression hypothesis
* Debye–Hückel–Onsager equation
* Onsager reciprocal relations
* Square lattice Ising model
* Revealing the physics behind the De Haas–van Alphen effect and the Wien effect

Awards|

* Lorentz Medal (1958)
* Willard Gibbs Award (1962)
* Peter Debye Award (1965)
* Nobel Prize in Chemistry (1968)
* National Medal of Science (1968)
* ForMemRS (1975)[1]

Scientific career
Fields| Physical chemist
Institutions|

* ETH Zürich
* Johns Hopkins University
* Brown University
* Yale University
* University of Miami

Thesis| Solutions of the Mathieu Equation of Period 4π and Certain Related Functions (1935)
Doctoral students| Joseph L. McCauley[2]

Lars Onsager (November 27, 1903 - October 5, 1976)[1] was a Norwegian American physical chemist and theoretical physicist. He held the Gibbs Professorship of Theoretical Chemistry at Yale University. He was awarded the Nobel Prize in Chemistry in 1968.[3][4][5]

## Contents

* 1 Education and early life
* 2 Career and research
* 2.1 Johns Hopkins University
* 2.2 Brown University
* 2.3 Yale University
* 2.4 After Yale
* 3 Research
* 3.1 Exact solution of the 2D Ising model
* 4 Personal life
* 4.1 Legacy
* 5 See also
* 6 References
* 7 External links
* 7.1 Archival collections

## Education and early life

Lars Onsager was born in Kristiania (now Oslo), Norway. His father was a lawyer. After completing secondary school in Oslo, he attended the Norwegian Institute of Technology (NTH) in Trondheim, graduating as a chemical engineer in 1925. While there he worked through A Course of Modern Analysis, which was instrumental in his later work.

## Career and research

In 1925 he arrived at a correction to the Debye-Hückel theory of electrolytic solutions, to specify Brownian movement of ions in solution, and during 1926 published it. He traveled to Zürich, where Peter Debye was teaching, and confronted Debye, telling him his theory was wrong. He impressed Debye so much that he was invited to become Debye's assistant at the Eidgenössische Technische Hochschule (ETH), where he remained until 1928.[6]

### Johns Hopkins University

In 1928 he went to the United States to take a faculty position at the Johns Hopkins University in Baltimore, Maryland. At JHU he had to teach freshman classes in chemistry, and it quickly became apparent that, while he was a genius at developing theories in physical chemistry, he had little talent for teaching. He was dismissed by JHU after one semester.[7]

### Brown University

On leaving JHU, he accepted a position (involving the teaching of statistical mechanics to graduate students in chemistry) at Brown University in Providence, Rhode Island, where it became clear that he was no better at teaching advanced students than freshmen, but he made significant contributions to statistical mechanics and thermodynamics. His graduate student Raymond Fuoss worked under him and eventually joined him on the Yale chemistry faculty. His statistical mechanics course was nicknamed "Sadistical Mechanics" by the students.[8]

His research at Brown was concerned mainly with the effects on diffusion of temperature gradients, and produced the Onsager reciprocal relations in statistical mechanics, a set of equations published in 1929 and, in an expanded form, in 1931, whose importance went unrecognized for many years. However, their value became apparent during the decades following World War II, and by 1968 they were considered important enough to gain Onsager that year's Nobel Prize in Chemistry.

In 1933, when the Great Depression limited Brown's ability to support a faculty member who was only useful as a researcher and not a teacher, he was let go by Brown. He traveled to Austria to visit electrochemist Hans Falkenhagen. He met Falkenhagen's sister-in-law, Margrethe Arledter. They were married on September 7, 1933, and had three sons and a daughter.[9]

### Yale University

After the trip to Europe, he was hired by Yale University, where he remained for most of the rest of his life, retiring in 1972.[10]

At Yale, he had been hired as a postdoctoral fellow, but it was discovered that he had never received a Ph.D.[3] While he had submitted an outline of his work in reciprocal relations to the Norwegian Institute of Technology, they had decided it was too incomplete to qualify as a doctoral dissertation. He was told that he could submit one of his published papers to the Yale faculty as a dissertation, but insisted on doing a new research project instead. His dissertation laid the mathematical background for his interpretation of deviations from Ohm's law in weak electrolytes.[11] It dealt with the solutions of the Mathieu equation of period 4π and certain related functions and was beyond the comprehension of the chemistry and physics faculty. Only when some members of the mathematics department, including the chairman Einar Hille (who also liked A Course of Modern Analysis), insisted that the work was good enough that they would grant the doctorate if the chemistry department would not, was he granted a Ph.D. in chemistry in 1935.

Even before the dissertation was finished, he was appointed assistant professor in 1934,[3] and promoted to associate professor in 1940. He quickly showed at Yale the same traits he had at JHU and Brown: he produced brilliant theoretical research, but was incapable of giving a lecture at a level that a student (even a graduate student) could comprehend. He was also unable to direct the research of graduate students, except for the occasional outstanding one.[12] His two courses on statistical mechanics were nicknamed "Advanced Norwegian I" and "Advanced Norwegian II" for being incomprehensible.[8]

During the late 1930s, Onsager researched the dipole theory of dielectrics, making improvements for another topic that had been studied by Peter Debye. However, when he submitted his paper to a journal that Debye edited in 1936, it was rejected. Debye would not accept Onsager's ideas until after World War II. During the 1940s, Onsager studied the statistical-mechanical theory of phase transitions in solids, deriving a mathematically elegant theory which was enthusiastically received. In what is widely considered a tour de force of mathematical physics, he obtained the exact solution for the two dimensional Ising model in zero field in 1944.[13][14][15]

In 1960 he was awarded an honorary degree, doctor techn. honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology.[16]

In 1945, Onsager was naturalized as an American citizen, and the same year he was awarded the title of J. Willard Gibbs Professor of Theoretical Chemistry. This was particularly appropriate because Onsager, like Willard Gibbs, had been involved primarily in the application of mathematics to problems in physics and chemistry and, in a sense, could be considered to be continuing in the same areas Gibbs had pioneered. In 1947, he was elected to the National Academy of Sciences,[17] the American Academy of Arts and Sciences in 1949,[18] and in 1950 he joined the ranks of Alpha Chi Sigma.

After World War II, Onsager researched new topics of interest. He proposed a theoretical explanation of the superfluid properties of liquid helium in 1949; two years later the physicist Richard Feynman independently proposed the same theory. He also worked on the theories of liquid crystals and the electrical properties of ice. While on a Fulbright scholarship to the University of Cambridge, he worked on the magnetic properties of metals. He developed important ideas on the quantization of magnetic flux in metals. He was awarded the Lorentz Medal in 1958, Willard Gibbs Award in 1962,[19] and the Nobel Prize in Chemistry in 1968. He was elected a member of the American Philosophical Society in 1959 and a Foreign Member of the Royal Society (ForMemRS) in 1975.[20][1]

### After Yale

Graves of Onsager and Kirkwood

In 1972 Onsager retired from Yale and became emeritus. He then became a member of the Center for Theoretical Studies, University of Miami, and was appointed Distinguished University Professor of Physics.[21] At the University of Miami he remained active in guiding and inspiring postdoctoral students as his teaching skills, although not his lecturing skills, had improved during the course of his career. He developed interests in semiconductor physics, biophysics and radiation chemistry. However, his death came before he could produce any breakthroughs comparable to those of his earlier years.

## Research

### Exact solution of the 2D Ising model

To solve the 2D Ising model, Onsager began by diagonalizing increasingly large transfer matrices. He said that it's because he had a lot of time during WWII. He began by computing the 2 × 2 transfer matrix of the 1D Ising model, which is already solved by Ising himself. He then computed the transfer matrix of the "Ising ladder", meaning two 1D Ising models side-by-side, connected by links. The transfer matrix is then 4 × 4\. He repeated this for up to six 1D Ising models, resulting in transfer matrices of up to 64 × 64\. He diagonalized all of them and found that all the eigenvalues were of a special form, so he guessed that the algebra of the problem was an associative algebra (later called the Onsager algebra[22]).[23]

The solution involved generalized quaternion algebra and the theory of elliptic functions, which he learned from A Course of Modern Analysis.[7]

## Personal life

He remained in Florida until his death from an aneurysm in Coral Gables, Florida in 1976. Onsager was buried next to John Gamble Kirkwood at New Haven's Grove Street Cemetery. While Kirkwood's tombstone has a long list of awards and positions, including the American Chemical Society Award in Pure Chemistry, the Richards Medal, and the Lewis Award, Onsager's tombstone, in its original form, simply said "Nobel Laureate". When Onsager's wife Gretel died in 1991 and was buried there, his children added an asterisk after "Nobel Laureate" and "*etc." in the lower right corner of the stone.[24] He was identified as a Protestant.[25]

### Legacy

The Norwegian Institute of Technology established the Lars Onsager Lecture and The Lars Onsager Professorship in 1993 to award outstanding scientists in the scientific fields of Lars Onsager; Chemistry, Physics and Mathematics.[26] The American Physical Society established Lars Onsager Prize in statistical physics in 1993. In 1997 his sons and daughter donated his scientific works and professional belongings to NTNU (before 1996 NTH) in Trondheim, Norway as his alma mater. These are now organized as The Lars Onsager Archive at the Gunnerus Library in Trondheim.[27][28]

## See also

* Lattice density functional theory (1944) solution to a two-dimensional (2D) lattice problem

## References

1. ↑ 1.0 1.1 1.2 Longuet-Higgins, H. C.; Fisher, M. E. (1978). "Lars Onsager. 27 November 1903-5 October 1976". Biographical Memoirs of Fellows of the Royal Society 24: 443–471. doi:10.1098/rsbm.1978.0014. ISSN 0080-4606.
2. ↑ Lars Onsager at the Mathematics Genealogy Project
3. ↑ 3.0 3.1 3.2 Montroll, Elliott W. (February 1977). "Lars Onsager". Physics Today 30 (2): 77. doi:10.1063/1.3037438. Bibcode: 1977PhT....30b..77M. http://www.physicstoday.org/resource/1/phtoad/v30/i2/p77_s1?bypassSSO=1.
4. ↑ "The Nobel Prize in Chemistry 1968". https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1968/.
5. ↑ Per Chr Hemmer, ed (1996). World Scientific Series in 20th Century Physics: Volume 17 : The Collected Works of Lars Onsager. 17. doi:10.1142/3027. ISBN 978-981-02-2563-6. https://archive.org/details/collectedworksof0000onsa.
6. ↑ "Lars Onsager - Biographical". https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1968/onsager-bio.html.
7. ↑ 7.0 7.1 Christopher Longuet-Higgins, H.; Fisher, Michael E. (1995-01-01). "Lars Onsager: November 27, 1903–October 5, 1976" (in en). Journal of Statistical Physics 78 (1): 605–640. doi:10.1007/BF02183371. ISSN 1572-9613. Bibcode: 1995JSP....78..605C. https://doi.org/10.1007/BF02183371.
8. ↑ 8.0 8.1 Christopher Longuet-Higgins, H.; Fisher, Michael E. (1995-01-01). "Lars Onsager: November 27, 1903–October 5, 1976" (in en). Journal of Statistical Physics 78 (1): 605–640. doi:10.1007/BF02183371. ISSN 1572-9613. Bibcode: 1995JSP....78..605C. https://doi.org/10.1007/BF02183371.
9. ↑ "Lars Onsager – Norsk biografisk leksikon". 1991-12-06. https://nbl.snl.no/Lars_Onsager.
10. ↑ "Lars Onsager". http://www.nndb.com/people/579/000100279/.
11. ↑ Onsager, Lars (1934-09-01). "Deviations from Ohm's Law in Weak Electrolytes" (in en). The Journal of Chemical Physics 2 (9): 599–615. doi:10.1063/1.1749541. ISSN 0021-9606. Bibcode: 1934JChPh...2..599O. https://pubs.aip.org/jcp/article/2/9/599/201481/Deviations-from-Ohm-s-Law-in-Weak-Electrolytes.
12. ↑ "Famous Chemists Web Site". http://emur.org/chemists/lars-onsager.htm.
13. ↑ "Lars Onsager | Array of Contemporary American Physicists". http://www.aip.org/history/acap/biographies/bio.jsp?onsagerl.
14. ↑ "index.htm". http://faculty.cua.edu/may/.
15. ↑ Onsager, Lars (1944). "Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition". Physical Review 65 (3–4): 117–149. doi:10.1103/PhysRev.65.117. Bibcode: 1944PhRv...65..117O.
16. ↑ "Honorary doctors at NTNU" (in en). Norwegian University of Science and Technology. http://www.ntnu.edu/phd/honorary-doctors.
17. ↑ "Lars Onsager". http://www.nasonline.org/member-directory/deceased-members/20001605.html.
18. ↑ "Lars Onsager" (in en). https://www.amacad.org/person/lars-onsager.
19. ↑ "Willard Gibbs Award". http://chicagoacs.org/content.php?page=Willard_Gibbs_Award.
20. ↑ "APS Member History". https://search.amphilsoc.org/memhist/search?creator=Lars+Onsager&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced.
21. ↑ National Academy of Sciences (1991). "Lars Onsager". Biographical Memoirs. 60. The National Academies Press. doi:10.17226/6061. ISBN 978-0-309-07865-8. http://www.nap.edu/openbook.php?record_id=6061&page=218. Retrieved 2016-03-07.
22. ↑ Davies, B. (June 1990). "Onsager's algebra and superintegrability" (in en). Journal of Physics A: Mathematical and General 23 (12): 2245–2261. doi:10.1088/0305-4470/23/12/010. ISSN 0305-4470. Bibcode: 1990JPhA...23.2245D. https://dx.doi.org/10.1088/0305-4470/23/12/010.
23. ↑ Chen-Ning Yang, Selected papers (1945–1980) of Chen Ning Yang With Commentary, World Scientific Series in 20th Century Physics: Volume 36 (2005), paper and commentary [52a]. pp. 11-13
24. ↑ "Grove Street Cemetery". Grove Street Cemetery. 2003-08-06. http://www.grovestreetcemetery.org/self_guided_grove_street_cemetery_tours.htm.
25. ↑ Sherby, Louise S. (2001-12-30). The Who’s Who of Nobel Prize Winners 1901–2000. Oryx Press. p. 29. ISBN 1573564141.
26. ↑ "Onsager". 2015-08-28. http://www.ntnu.edu/onsager.
27. ↑ "Onsager biography". http://www.ntnu.no/ub/spesialsamlingene/tekark/tek5/notes_on_biography.php.
28. ↑ "Prof. Dr. Lars Onsager". 12 May 2014. http://www.mediatheque.lindau-nobel.org/laureates/onsager.

## External links

| Wikimedia Commons has media related to Lars Onsager.

|

* Lars Onsager papers (MS 794). Manuscripts and Archives, Yale University Library. [1]
* The Lars Onsager Lecture and Professorship (Norwegian University of Science And Technology)
* The Onsager Committee (Norwegian University of Science And Technology)
* The Lars Onsager Lecture and The Lars Onsager Professorship (Norwegian University of Science And Technology).
* The Motion of Ions: Principles and Concepts (Lars Onsager's Nobel Lecture)

### Archival collections

* The Lars Onsager Online Archive at Universitetsbiblioteket/Gunnerus Library in Trondheim. (Norwegian University of Science And Technology)
* Alvin M. Saperstein student notes on lectures by Lars Onsager and Cecil T. Lane, 1952-1953, Niels Bohr Library & Archives
* George O. Zimmerman collection of lecture notes by Gregory Breit and Lars Onsager, circa 1960-1961, Niels Bohr Library & Archives
* Lars Onsager papers, Manuscripts and Archives Department Yale University Library

* v
* t
* e

Laureates of the Nobel Prize in Chemistry

1901–1925|

* 1901: Jacobus van 't Hoff
* 1902: Emil Fischer
* 1903: Svante Arrhenius
* 1904: William Ramsay
* 1905: Adolf von Baeyer
* 1906: Henri Moissan
* 1907: Eduard Buchner
* 1908: Ernest Rutherford
* 1909: Wilhelm Ostwald
* 1910: Otto Wallach
* 1911: Marie Curie
* 1912: Victor Grignard / Paul Sabatier
* 1913: Alfred Werner
* 1914: Theodore Richards
* 1915: Richard Willstätter
* 1916
* 1917
* 1918: Fritz Haber
* 1919
* 1920: Walther Nernst
* 1921: Frederick Soddy
* 1922: Francis Aston
* 1923: Fritz Pregl
* 1924
* 1925: Richard Zsigmondy

1926–1950|

* 1926: Theodor Svedberg
* 1927: Heinrich Wieland
* 1928: Adolf Windaus
* 1929: Arthur Harden / Hans von Euler-Chelpin
* 1930: Hans Fischer
* 1931: Carl Bosch / Friedrich Bergius
* 1932: Irving Langmuir
* 1933
* 1934: Harold Urey
* 1935: Frédéric Joliot-Curie / Irène Joliot-Curie
* 1936: Peter Debye
* 1937: Norman Haworth / Paul Karrer
* 1938: Richard Kuhn
* 1939: Adolf Butenandt / Leopold Ružička
* 1940
* 1941
* 1942
* 1943: George de Hevesy
* 1944: Otto Hahn
* 1945: Artturi Virtanen
* 1946: James B. Sumner / John Northrop / Wendell Meredith Stanley
* 1947: Robert Robinson
* 1948: Arne Tiselius
* 1949: William Giauque
* 1950: Otto Diels / Kurt Alder

1951–1975|

* 1951: Edwin McMillan / Glenn T. Seaborg
* 1952: Archer Martin / Richard Synge
* 1953: Hermann Staudinger
* 1954: Linus Pauling
* 1955: Vincent du Vigneaud
* 1956: Cyril Hinshelwood / Nikolay Semyonov
* 1957: Alexander Todd
* 1958: Frederick Sanger
* 1959: Jaroslav Heyrovský
* 1960: Willard Libby
* 1961: Melvin Calvin
* 1962: Max Perutz / John Kendrew
* 1963: Karl Ziegler / Giulio Natta
* 1964: Dorothy Hodgkin
* 1965: Robert Woodward
* 1966: Robert S. Mulliken
* 1967: Manfred Eigen / Ronald Norrish / George Porter
* 1968: Lars Onsager
* 1969: Derek Barton / Odd Hassel
* 1970: Luis Federico Leloir
* 1971: Gerhard Herzberg
* 1972: Christian B. Anfinsen / Stanford Moore / William Stein
* 1973: Ernst Otto Fischer / Geoffrey Wilkinson
* 1974: Paul Flory
* 1975: John Cornforth / Vladimir Prelog

1976–2000|

* 1976: William Lipscomb
* 1977: Ilya Prigogine
* 1978: Peter D. Mitchell
* 1979: Herbert C. Brown / Georg Wittig
* 1980: Paul Berg / Walter Gilbert / Frederick Sanger
* 1981: Kenichi Fukui / Roald Hoffmann
* 1982: Aaron Klug
* 1983: Henry Taube
* 1984: Robert Merrifield
* 1985: Herbert A. Hauptman / Jerome Karle
* 1986: Dudley R. Herschbach / Yuan T. Lee / John Polanyi
* 1987: Donald J. Cram / Jean-Marie Lehn / Charles J. Pedersen
* 1988: Johann Deisenhofer / Robert Huber / Hartmut Michel
* 1989: Sidney Altman / Thomas Cech
* 1990: Elias Corey
* 1991: Richard R. Ernst
* 1992: Rudolph A. Marcus
* 1993: Kary Mullis / Michael Smith
* 1994: George Olah
* 1995: Paul J. Crutzen / Mario J. Molina / F. Sherwood Rowland
* 1996: Robert Curl / Harold Kroto / Richard Smalley
* 1997: Paul D. Boyer / John E. Walker / Jens Christian Skou
* 1998: Walter Kohn / John Pople
* 1999: Ahmed Zewail
* 2000: Alan J. Heeger / Alan MacDiarmid / Hideki Shirakawa

2001–present|

* 2001: William Knowles / Ryoji Noyori / K. Barry Sharpless
* 2002: John B. Fenn / Koichi Tanaka / Kurt Wüthrich
* 2003: Peter Agre / Roderick MacKinnon
* 2004: Aaron Ciechanover / Avram Hershko / Irwin Rose
* 2005: Robert H. Grubbs / Richard R. Schrock / Yves Chauvin
* 2006: Roger D. Kornberg
* 2007: Gerhard Ertl
* 2008: Osamu Shimomura / Martin Chalfie / Roger Y. Tsien
* 2009: Venkatraman Ramakrishnan / Thomas A. Steitz / Ada E. Yonath
* 2010: Richard F. Heck / Akira Suzuki / Ei-ichi Negishi
* 2011: Dan Shechtman
* 2012: Robert Lefkowitz / Brian Kobilka
* 2013: Martin Karplus / Michael Levitt / Arieh Warshel
* 2014: Eric Betzig / Stefan Hell / William E. Moerner
* 2015: Tomas Lindahl / Paul L. Modrich / Aziz Sancar
* 2016: Jean-Pierre Sauvage / Fraser Stoddart / Ben Feringa
* 2017: Jacques Dubochet / Joachim Frank / Richard Henderson
* 2018: Frances Arnold / Gregory Winter / George Smith
* 2019: John B. Goodenough / M. Stanley Whittingham / Akira Yoshino

* v
* t
* e

1968 Nobel Prize laureates

Chemistry|

* Lars Onsager (Great Britain)

Literature|

* Yasunari Kawabata (Japan)

Peace|

* René Cassin (France)

Physics|

* Luis Walter Alvarez (United States)

Physiology or Medicine|

* Robert W. Holley (United States)
* Har Gobind Khorana (United States)
* Marshall Warren Nirenberg (United States)

Nobel Prize recipients
1990

2000

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