Inverse Design of Non-Equilibrium Steady-States: A Large Deviation Approach

TL;DR

This paper introduces a large deviation-based method for designing complex non-equilibrium steady states by controlling force fields, enabling the creation of intricate density and flux patterns in Brownian systems.

Contribution

It presents a novel approach leveraging large deviation functionals and a relaxation algorithm to design non-equilibrium steady states with complex geometries, filling a gap in non-equilibrium thermodynamics.

Findings

Successfully replicates analytical results

Generates complex shapes like roses and polygons

Demonstrates the method's versatility and potential

Abstract

The design of small scale non-equilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for non-equilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large deviation functional for the empirical density and flow, and a "relaxation" algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking.