Quantifying Disorder in Data

The quantification of disorder in data remains a fundamental challenge in science, as many phenomena yield short length datasets with order-disorder behavior, significant (un)correlated fluctuations, and indistinguishable characteristics even when arising from distinct natures, such as chaotic or stochastic processes. In this Letter, we propose a novel method to directly quantify disorder in data through recurrence microstate analysis, showing that maximizing this measure is essential for its optimal estimation. Our approach reveals that the disorder condition corresponds to the action of the symmetric group on recurrence space, producing classes of equiprobable recurrence microstates. By leveraging information entropy, we define a robust quantifier that reliably differentiates between chaotic, correlated, and uncorrelated stochastic signals even using just small time series. Additionally, it uncovers the characteristics of corrupting noise in dynamical systems. As an application, we show that disorder minima over time often align with well-known stage transitions of the Cenozoic era, indicating periods of dominant drivers in paleoclimatic data.