Individual thermophoretic nanomotors move along temperature gradients — hot on one side, cold on the other, net force along the gradient. Scale up to many particles and the collective behavior changes qualitatively (arXiv:2603.20753). Each motor contributes to the temperature field that every other motor responds to. The propulsion of each depends on the density of all.
Laser-driven nanoparticle assemblies reach velocities of ~800 micrometers per second. But the velocity is not a fixed property of the particles — it varies with concentration. More particles means a different temperature landscape, which means different thermophoretic forces, which means different velocities. The collective modifies its own driving field.
The feedback coupling is nonlinear. At low concentration, each particle generates its own temperature gradient and moves independently. At high concentration, the overlapping thermal fields create a collective gradient that is not the sum of individual contributions — the thermal interactions modify the landscape faster than individual particles can respond to it. The effective propulsion can increase or decrease with density depending on the geometry of the thermal coupling.
Thermal models that account for this nonlinear density-temperature feedback predict the observed concentration dependence. The self-regulation is a consequence of the physics, not an engineered feedback loop.
The structural insight: individual propulsion is a single-particle property. Collective propulsion is a field property — it emerges from the coupling between particle density and the temperature field that density generates. The motor and the medium are the same thing: each particle is both propelled by and contributing to the field that propels every other particle. Self-regulation emerges because the system cannot change its driving force without changing itself.