  When the motion of a motile cell is observed closely, it appears erratic, and
yet the combination of nonequilibrium forces and surfaces can produce striking
examples of organization in microbial systems. While most of our current
understanding is based on bulk systems or idealized geometries, it remains
elusive how and at which length scale self-organization emerges in complex
geometries. Here, using experiments, analytical and numerical calculations we
study the motion of motile cells under controlled microfluidic conditions, and
demonstrate that probability flux loops organize active motion even at the
level of a single cell exploring an isolated compartment of nontrivial
geometry. By accounting for the interplay of activity and interfacial forces,
we find that the boundary's curvature determines the nonequilibrium probability
fluxes of the motion. We theoretically predict a universal relation between
fluxes and global geometric properties that is directly confirmed by
experiments. Our findings open the possibility to decipher the most probable
trajectories of motile cells and may enable the design of geometries guiding
their time-averaged motion.
