Self-Consistent Closure of Fractal Dimension, Nonextensive Statistics, and Non-Markovian Dynamics in Critical Systems (opens in new tab)

Self-organized critical systems often exhibit three macroscopic features simultaneously: nonextensive thermodynamics (quantified by the Tsallis index $q$), structural fractality (measured by the Hausdorff dimension $D$), and non-Markovian dynamics (characterized by the memory exponent $\alpha$). Historically, these parameters have been treated as independent, to be empirically fitted case by case. Here we demonstrate that phase-space self-consis...