Probing the Theoretical and Computational Limits of Dissipative Design

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.

References in corpus (8)

• Motility-Induced Phase Separation
• Designed Interaction Potentials via Inverse Methods for Self-Assembly
• Self-assembly of the simple cubic lattice with an isotropic potential
• Designing patchy interactions to self-assemble arbitrary structures
• Growth of equilibrium structures built from a large number of distinct component types
• Variational design principles for nonequilibrium colloidal assembly
• Optimized Large Hyperuniform Binary Colloidal Suspensions in Two Dimensions
• Minimum Power to Maintain a Nonequilibrium Distribution of a Markov Chain

Cited by in corpus (2)

• Energetic cost of feedback control
• Reinforcement Learning reveals fundamental limits on the mixing of active particles