  We investigate to what extent one can use a thermodynamic description of
turbulent flow as a source of stochastic kinetic energy for three-dimensional
self-assembly of magnetically interacting macroscopic particles. We confirm
that the speed of the objects in the flow field generated in our system obeys
the Maxwell--Boltzmann distribution, and their random walk can be defined by a
diffusion coefficient following from the Einstein relation. However, we
discovered that the analogy with Brownian dynamics breaks down when considering
the directional components of the velocity. For the vectorial components,
neither the equipartition theorem, nor the Einstein relation is obeyed.
Moreover, the kinetic energy estimated from the random walk of individual
objects is one order of magnitude higher than the value estimated from
Boltzmann statistics on the interaction between two spheres with embedded
magnets. These results show that introducing stochastic kinetic energy into a
self-assembly process by means of turbulent flow can to a great extent be
described by standard thermodynamic theory, but anisotropies and the specific
nature of the interactions need to be taken into account.
