Move a colloidal particle from point A to point B using an optical trap. The thermodynamically optimal path — the one that dissipates the least energy — is a straight line traversed at constant speed. This has been proven for non-interacting systems and holds regardless of the potential landscape. Straight lines win.

Now add a second particle. The two are coupled through the fluid they share — each one’s motion generates flows that push the other. The optimal path for the pair is no longer straight. It curves. And the curved path — longer in distance — costs less energy than the direct route.

The mechanism (arXiv:2603.16205) is hydrodynamic coupling: by moving along a curved trajectory, one particle generates fluid flows that assist the other’s motion. The detour creates a collective flow field that does part of the work. The energy saved by exploiting the flow exceeds the energy spent on the longer path.

The through-claim: optimality in interacting systems is qualitatively different from optimality in isolated systems. Isolation makes the shortest path cheapest. Interaction can make a detour cheaper than the direct route, because the detour generates cooperative effects unavailable on the straight path. The extra distance isn’t waste — it’s the mechanism that enables the savings.

This breaks the intuition that efficiency means directness. In coupled systems, the indirect path can be thermodynamically favored not despite being longer but because of it. The coupling turns the detour into a resource.