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 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 call quantropy. 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.