Lars Onsager and Irreversible Chemical Processes

Lars Onsager (1903-1976)

Lars Onsager (1903-1976) [7]

On November 27, 1903, Norwegian-born American physical chemist and theoretical physicist Lars Onsager was born. The development of a general theory of irreversible chemical processes gained him the 1968 Nobel Prize for Chemistry. These Onsager reciprocal relations have importance in a wide range of applications.


Lars Onsager was born in Kristiania (today’s Oslo), Norway, to Erling Onsager, a Barrister of the Supreme Court of Norway, and Ingrid, née Kirkeby. After completing secondary school in Oslo in 1920, where he was invited to jump a grade, he attended the Norwegian Institute of Technology (NTH) in Trondheim, graduating as a chemical engineer in 1925. Among the professors particularly O.E. Collenberg and J.P. Holtsmark encouraged his efforts in theory and helped him in the evaluation of background knowledge.[1] From 1926 to 1928 he worked as a research assistant at ETH Zurich with theoretical chemist and Nobel laureate Peter Debye.

Academic Career in the USA

Eventually 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. The appointment was not renewed; but C.A. Kraus at Brown University in Providence, Rhode Island, engaged him as an instructor teaching ostatistical mechanics to graduate students in chemistry, and he remained in that position for five years.[1] It became clear that he was no better at teaching advanced students than freshmen, but he made significant contributions to statistical mechanics and thermodynamics. 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, being hired by Yale University, where he remained for most of the rest of his life, retiring in 1972.

Research in Thermodynamics

His research at Brown was concerned mainly with the effects on diffusion of temperature gradients, and produced the Onsager reciprocal relations, a set of equations published in 1929 and, in an expanded form, in 1931, in statistical mechanics whose importance went unrecognized for many years. In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists. “Reciprocal relations” occur between different pairs of forces and flows in a variety of physical systems. For example, consider fluid systems described in terms of temperature, matter density, and pressure. In this class of systems, it is known that temperature differences lead to heat flows from the warmer to the colder parts of the system; similarly, pressure differences will lead to matter flow from high-pressure to low-pressure regions. What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow (as in convection) and pressure differences at constant temperature can cause heat flow. Perhaps surprisingly, the heat flow per unit of pressure difference and the density (matter) flow per unit of temperature difference are equal. This equality was shown to be necessary by Lars Onsager using statistical mechanics as a consequence of the time reversibility of microscopic dynamics (microscopic reversibility).

Difficulties in Obtaining the PhD and the Nobel Prize in Chemistry

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.At Yale, an embarrassing situation occurred: he had been hired as a postdoctoral fellow, but it was discovered that he had never received a Ph.D. 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, entitled, “Solutions of the Mathieu equation of period 4 pi and certain related functions“, was beyond the comprehension of the chemistry and physics faculty, and only when some members of the mathematics department, including the chairman, 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, 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.

Further Research

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. He obtained the exact solution for the two dimensional Ising model in zero field in 1944. 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. In 1947, he was elected to the National Academy of Sciences. 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. He was elected a Foreign Member of the Royal Society (ForMemRS) in 1975.

Lars Onsager died in Coral Gables, Florida in 1976, aged 72.

JDG 2017: Camille de Lellis: The Onsager Theorem, [8]

References and Further Reading:

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