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A study of the ‘irreversibility paradox’ for a simple statistical assembly

Published online by Cambridge University Press:  24 October 2008

H. N. V. Temperley
H. N. V. Temperley
Affiliation:
Atomic Weapons Research EstablishmentAldermastonBerkshire
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Abstract

A very simple model, consisting of N particles moving in a one-dimensional assembly divided by potential ‘humps’ into M cells, is studied. The process of passing from a quantum-mechanical description of such an assembly to the equation of diffusion type that governs it in practice is shown to consist of at least three separate steps: ‘averaging over phases’, and letting N and M become large. The effects of these steps are considered separately. Strict irreversibility in time appears after the first step, but the assembly remains ergodic until after the second step and fluctuations persist until after the third step.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 712 - 718
Copyright
Copyright © Cambridge Philosophical Society 1956

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References

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