Partition function (mathematics): Difference between revisions

Revision as of 20:17, 10 July 2012

Revision as of 05:51, 15 July 2012

Line 138:

where we've written <math>P(x)</math> for <math>P(x_1,x_2,\dots)</math> and the summation is understood to be over all values of all random variables <math>X_k</math>. For continuous-valued random variables, the summations are replaced by integrals, of course.

Curiously, the [[Fisher information metric]] can also be understood as the flat-space [[Euclidean metric]], after appropriate change of variables, as described in the main article on it. When the <math>\beta</math> are complex-valued, the resulting metric is the [[Fubini-Study metric]]. When written in terms of [[mixed state (physics)|mixed states]], instead of [[pure state]]s, it is known as the [[Bures metric]].

The [[Bures metric]] is the quantum-mechanical analog of the Fisher information metric.

== Correlation functions==