Symbolic approach for measuring temporal "irreversibility"

We describe a symbolic approach for measuring temporal "irreversibility" in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements.