  There is demand in diverse fields for a reliable method of estimating the
entropy associated with correlations. The estimation of a unique entropy
directly from the Pearson correlation matrix has remained an open problem for
more than half a century. All existing approaches lack generality insofar as
they require thresholding choices that arbitrarily remove possibly important
information. Here we propose an objective procedure for directly estimating a
unique entropy of a general Pearson matrix. We show that upon rescaling the
Pearson matrix satisfies all necessary conditions for an analog of the von
Neumann entropy to be well defined. No thresholding is required. We demonstrate
the method by estimating the entropy from neuroimaging time series of the human
brain under the influence of a psychedelic.
