Abstract:

Given a graph , one can consider its Laplacian Matrix . In this talk, I will study two dynamical systems associated to on . One depends on the diffusion equation , which is related to the classical thermodynamics. The other depends on the Schördinger equation , which is related to the quantum dynamics. Then, I will compute the change of entropy of these two dynamical system on . The goal is to understand how the empirical entropy defined in the classical thermodynamics relates to the Boltzmann (Shannon) entropy defined in the quantum dynamic particularly on a discrete model.