  Recent microfluidic experiments revealed that large particles advected in a
fluidic loop display long-range hydrodynamic interactions. However, the
consequences of such couplings on the traffic dynamics in more complex networks
remain poorly understood. In this letter, we focus on the transport of a finite
number of particles in one-dimensional loop networks. By combining numerical,
theoretical, and experimental efforts, we evidence that this collective process
offers a unique example of Hamiltonian dynamics for hydrodynamically
interacting particles. In addition, we show that the asymptotic trajectories
are necessarily reciprocal despite the microscopic traffic rules explicitly
break the time reversal symmetry. We exploit these two remarkable properties to
account for the salient features of the effective three-particle interaction
induced by the exploration of fluidic loops.
