The European Physical Journal H

, Volume 35, Issue 2, pp 201–237

Proof of the ergodic theorem and the H-theorem in quantum mechanics

Translation of: Beweis des Ergodensatzes und des H-Theorems in der neuen Mechanik
  • J. von Neumann
Historical document

DOI: 10.1140/epjh/e2010-00008-5

Cite this article as:
von Neumann, J. EPJ H (2010) 35: 201. doi: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.

Supplementary material

Copyright information

© EDP Sciences and Springer 2010

Authors and Affiliations

  • J. von Neumann

There are no affiliations available

Personalised recommendations