Thermodynamic edge entropy in Alzheimer's disease

In this paper, we explore how to decompose the global thermodynamic entropy of a network into components associated with its edges. Commencing from a statistical mechanical picture, in which the normalised Laplacian matrix plays the role of Hamiltonian operator, thermodynamic entropy can be calculated from partition function associated with different energy level occupation distributions arising from Maxwell–Boltzmann statistics. Using the spectral decomposition of the Laplacian, we show how to project the edge-entropy components so that the detailed distribution of entropy across the edges of a network can be achieved. We apply the resulting method to the brain functional connectivity networks using BOLD-fMRI data. The entropic measurement turns out to be an effective tool for the diagnosis of Alzheimer's disease by finding the most salient functional connectivity features from the corresponding anatomical brain regions.