Agenda

Presenta: Edwin Hancock, University of York, UK

Abstract:
The heat-bath analogy has found widespread use in the analysis of network systems. Here the idea is to consider how the energy states associated with a network are populated when submerged in a heat-bath. Usually, this analysis is conducted under the assumption that particles moving in the energy landscape can populate the energy levels subject to classical Maxwell-Boltzmann statistics. In this talk, on the other hand,  we consider how thermodynamic quantities such as entropy and energy   are modified if the particles are subject to quantum spin statistics. Specifically if the particles have integer spin, then they are subject to Bose-Einstein statistics, while particles of half integer spin are subject to Fermi-Dirac statistics. The net effect of the latter is to restrict the occupation of each energy state to a single particle due to the exclusion principle. While in the case of the former, at low temperatures many particles can coalesce in the lowest energy state, giving rise to a Bose-Einstein condensate. Hence the energy and entropy associated with the system of particles associated with the network, tend to sample just the lowest eigenstates in the case of Bose-Einstein statistics, and higher eigenstates in the case of Fermi-Dirac statistics. We demonstrate some of the utility of the proposed methods on fMRI images of Alzheimer brains.