Probing the Theoretical and Computational Limits of Dissipative Design

TL;DR

This paper establishes a theoretical bound linking the accuracy of driven self-assembly to energetic costs and demonstrates how deep reinforcement learning can design protocols to stabilize complex, nonequilibrium states of matter.

Contribution

It derives a universal bound on dissipation versus target proximity in nonequilibrium self-assembly and shows deep reinforcement learning can effectively design control protocols.

Findings

High-dimensional control guides systems towards target states with entropic costs.

The derived bound applies arbitrarily far from equilibrium.

Deep reinforcement learning can realize complex protocols for stabilizing inaccessible states.

Abstract

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 \emph{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. Remarkably, the bound holds arbitrarily far from equilibrium. Secondly, we investigate the performance of deep reinforcement learning algorithms and provide evidence for the realizability of complex protocols that stabilize otherwise inaccessible states of matter.