When controlling a single particle in an optical trap, the most energy-efficient path between two configurations is a straight line traversed at constant speed. Monter, Stutzer, Loos, and Bechinger demonstrate experimentally that this intuition fails for collections of interacting colloidal particles: hydrodynamic coupling between particles can make curved paths consume less energy than straight ones.
The physics turns on the distinction between conservative and non-conservative interactions. For conservative forces -- where the interaction depends only on particle separation -- optimal trajectories remain linear in the low-noise limit, regardless of the specific potential. But hydrodynamic coupling is non-conservative: moving one particle generates fluid flows that act on its neighbors, and those flows depend on direction and speed, not just distance. When particles travel along curved trajectories, they generate flow patterns that assist each other's motion, effectively drafting through the surrounding fluid. The energy saved by exploiting these collective flows exceeds the energy cost of the longer path. The effect is robust in experiments and appears in both two-particle and multi-particle configurations.
This result reframes the relationship between optimality and directness in many-body control. Single-particle intuition equates efficiency with minimal displacement, but in interacting systems, the medium itself becomes a resource. The fluid transmits information between particles in the form of velocity fields, and the control problem becomes one of orchestrating those fields rather than simply minimizing individual distances. It is a concrete demonstration that optimal transport in interacting systems is fundamentally a collective phenomenon.
(arXiv:2603.16205)