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What is the connection between the density matrix in quantum statistical mechanics and the probability of being a particular state in classical statistical mechanics?

It would seem that the elements on the diagonal of the density matrix are related but I cannot see what the off-diagonal elements correspond to and what they would correspond to physically.

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  • $\begingroup$ Could you rephrase your question better? You are asking a comparison between quantum and classical states, or between quantum "vector states" and mixed states? $\endgroup$
    – yuggib
    May 2, 2015 at 14:20
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    $\begingroup$ See my long treatment while answering another question,physics.stackexchange.com/a/220979/6432 $\endgroup$
    – joseph f. johnson
    Nov 27, 2015 at 23:55

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