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The implications of the Ehrenfest theorem for systems with classically chaotic dynamics are discussed at Scholarpedia article Ehrenfest time and chaos. Due to exponential instability of classical trajectories the Ehrenfest time, on which there is a complete correspondence between quantum and classical evolution, is shown to be logarithmically ...
Paul Ehrenfest was born on 18 January 1880 in Vienna to Jewish parents, [3] who were originally from Loštice in Moravia (now part of the Czech Republic). His parents, Sigmund Ehrenfest and Johanna Jellinek, managed a grocery store. Although the family was not overly religious, Paul studied Hebrew and Jewish history. Later, he always emphasized ...
ISBN 978-1-4020-1805-3. This book contains a comprehensive historical survey by Øyvind Grøn, on which the "brief history" in this article is based, and some other papers on the Ehrenfest paradox and related controversies. Hundreds of additional references may be found in this book, particularly the paper by Grøn. Kumar, Jitendra (2024).
The book has three chapters. The first chapter, "Paul or the Discovery of the Irrational", written in the third person, is about physicist Paul Ehrenfest.The chapter opens with Ehrenfest shooting dead his son Vassily, who suffered from Down syndrome, and then himself.
[1]: 6–7 The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, [2] but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law. The phrase refers to the fact that the empirically derived Rayleigh–Jeans law, which accurately predicted experimental results at large wavelengths, failed to ...
The Timoshenko–Ehrenfest beam theory was developed by Stephen Timoshenko and Paul Ehrenfest [1] [2] [3] early in the 20th century. [ 4 ] [ 5 ] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams , or beams subject to high ...
Ehrenfest became the most important scientific influence in his life. From 1922 to 1925 Uhlenbeck was the tutor of the younger son of the Dutch ambassador in Rome . While there, he attended lectures by Tullio Levi-Civita and Vito Volterra and met his longtime friend, Enrico Fermi .
Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. The Clausius–Clapeyron relation does not make sense for second-order phase transitions, [ 1 ] as both specific entropy and specific volume do not change in second ...