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Entanglement and the foundations of statistical mechanics

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Abstract

Statistical mechanics is one of the most successful areas of physics. Yet, almost 150 years since its inception, its foundations and basic postulates are still the subject of debate. Here we suggest that the main postulate of statistical mechanics, the equal a priori probability postulate, should be abandoned as misleading and unnecessary. We argue that it should be replaced by a general canonical principle, whose physical content is fundamentally different from the postulate it replaces: it refers to individual states, rather than to ensemble or time averages. Furthermore, whereas the original postulate is an unprovable assumption, the principle we propose is mathematically proven. The key element in this proof is the quantum entanglement between the system and its environment. Our approach separates the issue of finding the canonical state from finding out how close a system is to it, allowing us to go even beyond the usual boltzmannian situation.

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Figure 1: The equiprobable state of the universe corresponding to the restriction R.
Figure 2: Bounding deviations from the average using Levy’s lemma.
Figure 3: Example: A system of spins.

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Acknowledgements

The authors would like to thank Y. Aharonov and N. Linden for discussions. S.P., A.J.S. and A.W. acknowledge support through the UK EPSRC project ‘QIP IRC’. In addition, S.P. also acknowledges support through EPSRC ‘Engineering-Physics’ grant GR/527405/01 and A.W. acknowledges a University of Bristol Research Fellowship.

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Authors and Affiliations

  1. H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

    Sandu Popescu & Anthony J. Short

  2. Hewlett-Packard Laboratories, Stoke Gifford, Bristol BS12 6QZ, UK

    Sandu Popescu

  3. Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK

    Andreas Winter

Authors
  1. Sandu Popescu
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  2. Anthony J. Short
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  3. Andreas Winter
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Correspondence to Anthony J. Short.

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Popescu, S., Short, A. & Winter, A. Entanglement and the foundations of statistical mechanics. Nature Phys 2, 754–758 (2006). https://doi.org/10.1038/nphys444

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