Spectral method for estimating entropy production rates in spatially extended systems

Due to the lack of symmetries and variational principles, non-equilibrium systems have been difficult to treat theoretically. Recent work has focused on measuring entropy production rates as a measure of a system's distance from equilibrium, but little connection has been made between entropy production and the complex, spatiotemporal dynamics that arise at different time and length-scales in driven systems. We present a generic method for estimating entropy production rates from stochastic time series data for both random variables and fields while providing insight into the dissipative processes underlying their dynamics. Our method provides insight into the relationship between pattern formation and dissipation in mesoscopic, driven reaction-diffusion systems. Importantly, this technique does not depend at all on the underlying system and can be used with data in any number of spatial dimensions.