Dynamical origin of quantum probabilities

We study the origin of the Born probability rule rho = \Psi\(2) in the de Broglie-Bohm pilot-wave formulation of quantum theory. It is argued that quantum probabilities arise dynamically, and have a status similar to thermal probabilities in ordinary statistical mechanics. This is illustrated by numerical simulations for a two-dimensional system. We show that a simple initial ensemble, with a non-standard distribution rho not equal \Psi\(2) of particle positions, evolves towards the quantum distribution to high accuracy. The relaxation process rho --> \Psi\(2) is quantified in terms of a coarse-grained H-function (equal to minus the relative entropy of rho with respect to \Psi\(2)), which is found to decrease approximately exponentially over time, with a time constant that accords with a simple theoretical estimate.