Ehrenfest
# Paul Ehrenfest

### Born: 18 Jan 1880
in Vienna, Austria

Died: 25 Sept 1933
in Leiden, Netherlands

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**Paul Ehrenfest** was a student at the Technische Hochschule in Vienna. There he formed a close friendship with three other students of mathematics, Heinrich Tietze, Hans Hahn and Herglotz. They called themselves the 'inseparable four'. Ehrenfest attended Boltzmann's lectures on the mechanical theory of heat during 1899-1900.
In 1901 he studied at Göttingen under Klein and Hilbert. There he took Max Abraham's course on the electromagnetic theory of light. He also attended courses by Stark, Walther Nernst, Schwarzschild and Zermelo.

Ehrenfest obtained his doctorate from Vienna in 1904, under Boltzmann's supervision, on a topic in classical mechanics. He returned to Göttingen in 1906 and there was influenced by Klein, Hilbert, Minkowski and Carathéodory.

In 1907 Ehrenfest went to St Petersburg. He was appointed to a chair to succeed Lorentz at the University of Leiden in 1912. Einstein was one of the main influences in Ehrenfest's appointment. They first met in Prague in 1912 and their deep friendship lasted until Ehrenfest's death. Ehrenfest was also a close friend of Niels Bohr.

Ehrenfest worked on quantum theory applying it to rotating bodies. He recognised that Ampère's molecular currents are incompatible with classical statistical mechanics. He proposed a model of diffusion in the early 1900s in order to illuminate the statistical interpretation of the second law of thermodynamics, that the entropy of a closed system can only increase. The modern theory of nonequilibrium thermodynamics brings together the molecular, collisional ideas of Boltzmann with the statistical ideas of Ehrenfest's to give a nonlinear, statistical theory.

Ehrenfest comitted suicide in 1933. Einstein said of Ehrenfest (see reference 2) that he was

the best teacher in our profession I have ever known.

**References (2 books/articles)**

JOC/EFR December 1996