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

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 make use of 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 of 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 those whose occupation and flux trace-out rose-curve or polygonal shapes. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where generalized frameworks are otherwise still lacking.