Inverse design of nonequilibrium steady states: A large-deviation approach

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