Abstract

Dragging a harmonic trap containing a single particle over a given distance in finite time is an elementary problem arising in experiments, theory and engineering applications. For a passive particle in a viscous medium, it is known that the optimal dragging protocol requiring the least amount of work has two symmetric jumps at the beginning and end. We show analytically, and confirm experimentally with light-trapped colloids in viscoelastic fluids [1], that time-reversal symmetry is an inherent property of this control problem. This symmetry holds universally for all types of media describable by a linear generalised Langevin equation, independent of the properties of the memory kernel and the coloured noise, including glassy, granular and active media. We further show that the optimal protocols for active particles are the same as for passive particles, while the work fluctuations are always increased [2].  [1] Loos, Monter, Ginot, Bechinger, Phys. Rev. X 14 , 021032 (2024).[2] Garcia-Millan, Schüttler, Cates, Loos, ArXiv:2407.18542 (2024).