Pearson matrices as density operators: a test of the entropic brain hypothesis using the von Neumann entropy

Abstract

The entropic brain hypothesis states that key functional parameters should exhibit increased entropy during psychedelic-induced altered brain states. This hypothesis has gained significant support over the years, particularly via thresholding Pearson correlation matrices of functional connectivity networks. However, the thresholding procedure is known to have drawbacks, mainly its arbitrariness in the threshold value selection. In this work, we propose an entirely objective, threshold-independent method of entropy estimation. Let R be a generic N ×N Pearson correlation matrix. We define ρ = R/N and prove that ρ satisfies the necessary conditions for a density operator. Therefore, the von Neumann entropy S = − tr(ρ ln ρ) can be directly calculated from the Pearson matrix. We then calculate the entropy of functional correlations of the human brain. Consistent with the entropic brain hypothesis, we find that entropy increases during the acute effects of the psychedelic Amazonian indigenous beverage ayahuasca.