Probing the Theoretical and Computational Limits of Dissipative Design

Self-assembly, the process by which interacting components form well-defined and often intricate structures, is typically thought of as a spontaneous process arising from equilibrium dynamics. When a system is driven by external nonequilibrium forces, states statistically inaccessible to the equilibrium dynamics can arise, a process sometimes termed direct self-assembly. However, if we fix a given target state and a set of external control variables, it is not well-understood i) how to design a protocol to drive the system towards the desired state nor ii) the energetic cost of persistently perturbing the stationary distribution. Here we derive a bound that relates the proximity to the chosen target with the dissipation associated with the external drive, showing that high-dimensional external control can guide systems towards target distribution but with an inevitable entropic cost. Secondly, we investigate the performance of deep multi-agent reinforcement learning algorithms and provide evidence for the realizability of complex protocols that stabilize otherwise inaccessible states of matter. Furthermore, we find that when agents share relevant information about the system, the learned protocols can more closely realize a given target state.