Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
History and Philosophy of Physics
2010-12-02 v2 Statistical Mechanics
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1003.2133,
title = {Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics},
author = {John von Neumann},
journal= {arXiv preprint arXiv:1003.2133},
year = {2010}
}
Comments
English translation by Roderich Tumulka of J. von Neumann: Beweis des Ergodensatzes und des H-Theorems. 41 pages LaTeX, no figures; v2: typos corrected. See also the accompanying commentary by S. Goldstein, J. L. Lebowitz, R. Tumulka, N. Zanghi, arXiv:1003.2129