  Numerical simulations indicate that the Born rule does not need to be
postulated in the de Broglie-Bohm pilot-wave theory, but arises dynamically
(relaxation to quantum equilibrium). These simulations were done for a particle
in a two-dimensional box whose wave-function obeys the non-relativistic
Schroedinger equation and is therefore scalar. The chaotic nature of the de
Broglie-Bohm trajectories, thanks to the nodes of the wave-function which act
as vortices, is crucial for a fast relaxation to quantum equilibrium. For
spinors, we typically do not expect any node. However, in the case of the Dirac
equation, the de Broglie-Bohm velocity field has vorticity even in the absence
of nodes. This observation raises the question of the origin of relaxation to
quantum equilibrium for fermions. In this article, we provide numerical
evidence to show that Dirac particles also undergo relaxation, by simulating
the evolution of various non-equilibrium distributions for two-dimensional
systems (the 2D Dirac oscillator and the Dirac particle in a spherical 2D box).
