  We show that Brownian motion is spatially not symmetric for mesoscopic
particles embedded in a fluid if the particle is not in thermal equilibrium and
its shape is not spherical. In view of applications on molecular motors in
biological cells, we sustain non-equilibrium by stopping a non-spherical
particle at periodic sites along a filament. Molecular dynamics simulations in
a Lennard-Jones fluid demonstrate that directed motion is possible without a
ratchet potential or temperature gradients if the asymmetric non-equilibrium
relaxation process is hindered by external stopping. Analytic calculations in
the ideal gas limit show that motion even against a fluid drift is possible and
that the direction of motion can be controlled by the shape of the particle,
which is completely characterized by tensorial Minkowski functionals.
