Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics

Details Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics

2010-03-10

arxiv.org/abs/1003.2133v2

European Phys. J. H 35: 201-237 (2010). German original in Zeitschrift fuer Physik 57: 30-70 (1929)

Physics

History and Philosophy of Physics

English translation by Roderich Tumulka of J. von Neumann: Beweis des Ergodensatzes und des H-Theorems. 41 pages LaTeX, no fig

Scientific paper

10.1140/epjh/e2010-00008-5

It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.

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