A Stochasticity-Chaos Analysis of Magnetar Flares, Glitches, Solar Flares, Earthquakes, FRBs and Repeating Source FRB 20240114A

Fast radio bursts (FRBs) are millisecond-duration cosmic transients whose origin remains elusive. Competing models invoke either earthquake-like processes or flare-like mechanisms. To discriminate between these scenarios, we compare the time–energy statistics of five large samples of repeating FRBs with those of magnetar flares, pulsar glitches, solar flares, and earthquakes. Utilizing two statistical diagnostics—the Pincus Index (PI) and the Lyapunov Exponent (LE)—we ascertain that FRBs occupy a distinct region in the stochasticity–chaos phase space. To assess the potential for temporal variations in source activity can shift a repeater's position in this phase space, we investigate the time evolution of the most prolific repeater, FRB 20240114A. Assembling the most comprehensive dataset to date, our work indicates that the radiation mechanisms of repeating FRBs are likely distinct from those driving magnetar flares, pulsar glitches, solar flares, or earthquakes. To conduct a comprehensive comparative study of the statistical properties of FRBs and other transients, we assemble event sequences that are as statistically rich as possible. All datasets used in this work are available in the data file. The interactive PLD Explorer enables users to further explore the Pincus–Lyapunov diagram (PLD) and interactively calculate PLD statistics using the available data.