Proof of the ergodic theorem and the H-theorem in quantum mechanics
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- von Neumann, J. EPJ H (2010) 35: 201. doi:10.1140/epjh/e2010-00008-5
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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.