It is well known that quantum mechanics in the path-integral form is formally very similar to equilibrium statistical mechanics formulated in terms of a partition function. In a relatively recent, very readable and straightforward paper(adsbygoogle = window.adsbygoogle || []).push({});

http://lanl.arxiv.org/abs/1311.0813

John Baez (a well known mathematical physicist) and Blake Pollard develop this formal analogy further by introducing a quantum analogy of entropy, which they callquantropy. I feel that this paper might be interesting and illuminating for many people on this forum.

Another reason for posting it is to make a concealed critique of AdS/CFT correspondence. This example demonstrates that, just because there is a mathematical correspondence between two theories, doesn't mean that the two theories really describe the same physics.

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# On the relation between quantum and statistical mechanics

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