Engineered swift equilibration for arbitrary geometries

TL;DR

This paper extends engineered swift equilibration (ESE) protocols to complex, curved configuration spaces, enabling rapid control of equilibrium distributions in a broad range of overdamped Brownian systems beyond simple geometries.

Contribution

We generalize ESE protocols to arbitrary curved configuration spaces, allowing precise control of distributions in complex systems previously inaccessible to existing methods.

Findings

Extended ESE to curved geometries.

Demonstrated control in non-Euclidean spaces.

Applicable to diverse experimental setups.

Abstract

Engineered swift equilibration (ESE) is a class of driving protocols that enforce an equilibrium distribution with respect to external control parameters at the beginning and end of rapid state transformations of open, classical non-equilibrium systems. ESE protocols have previously been derived and experimentally realized for Brownian particles in simple, one-dimensional, time-varying trapping potentials; one recent study considered ESE in two-dimensional Euclidean configuration space. Here we extend the ESE framework to generic, overdamped Brownian systems in arbitrary curved configuration space and illustrate our results with specific examples not amenable to previous techniques. Our approach may be used to impose the necessary dynamics to control the full temporal configurational distribution in a wide variety of experimentally realizable settings.