Fluctuations in biodiversity, both large and small, are pervasive through the fossil record, yet we do not understand the processes generating them. Here we use a novel extension of theory from non-equilibrium statistical physics to show that three universal properties of macroevolution--(i) heterogeneity of diversification rates between taxa, likely driven by (ii) niche conservatism and (iii) punctuated adaptive radiation--are sufficient to explain the previously unaccounted for fat-tailed form of fluctuations in diversity through the Phanerozoic... Using this theory, known as superstatistics, we identify taxonomic orders as largely autonomous evolutionary units, each likely experiencing its own unique and conserved region of an adaptive landscape. The separation of timescales between background origination and extinction compared to the origin of major ecological and evolutionary innovations between orders allow within-order dynamics to reach equilibrium, while between-order diversification is non-equilibrial, driven by major evolutionary innovations. Compared to other approaches that have used simple birth-death processes, equilibrial dynamics, or non-linear theories from complexity science, super-statistics is superior in its ability to account for both small and extreme fluctuations in fossil diversity. Its success opens up new research directions to better understand the universal nature of non-equilibrium dynamics across disparate systems of interest--from societal to physical to biological. Specifically in the biological case, research is motivated to understand the evolutionary processes leading to the stasis of order-level occupancy in an adaptive landscape punctuated by innovations between orders. (read more)