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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 ...
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special relativity , [ 1 ] it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. [ 2 ]
A similar equation describes the time evolution of the expectation values of observables, given by the Ehrenfest theorem. Corresponding to the trace-preserving property of the Schrödinger picture Lindblad equation, the Heisenberg picture equation is unital, i.e. it preserves the identity operator.
An example of breaking Born rigidity is the Ehrenfest paradox: Even though the state of uniform circular motion of a body is among the allowed Born rigid motions of class B, a body cannot be brought from any other state of motion into uniform circular motion without breaking the condition of Born rigidity during the phase in which the body ...
Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist who made major contributions to statistical mechanics and its relation to quantum mechanics, including the theory of phase transition [1] and the Ehrenfest theorem.
Taking expectation values automatically yields the Ehrenfest theorem, featured in the correspondence principle. By the Stone–von Neumann theorem , the Heisenberg picture and the Schrödinger picture are unitarily equivalent, just a basis change in Hilbert space .
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Paul and Tatjana Ehrenfest: Über zwei bekannte Einwände gegen das Boltzmannsche H-Theorem. Physikalische Zeitschrift, vol. 8 (1907), pp. 311–314. [1] F.P. Kelly: The Ehrenfest model, in Reversibility and Stochastic Networks. Wiley, Chichester, 1979. ISBN 0-471-27601-4 pp. 17–20. [3] David O. Siegmund: Ehrenfest model of diffusion ...