  Recently, the properties of bouncing oil droplets, also known as "walkers",
have attracted much attention because they are thought to offer a gateway to a
better understanding of quantum behaviour. They constitute indeed a macroscopic
realization of wave-particle duality, in the sense that their trajectories are
guided by a self-generated surrounding wave. The aim of this paper is to
develop a phenomenological theory for the behavior of walkers in terms of de
Broglie-Bohm and Nelson dynamics. We study in particular how modifications of
the de Broglie pilot-wave theory, \`a la Nelson, affect the process of
relaxation to quantum equilibrium, and prove an H-theorem for the relaxation to
quantum equilibrium under Nelson dynamics. We compare the onset of equilibrium
in the Nelson and de Broglie-Bohm approaches and we also propose some simple
experiments by which one can test the applicability of our theory to the
context of bouncing oil droplets.
