Left panel: evolution of the average kinetic luminosity, ﹩\langle {L}_{{\rm{K}}}\rangle ﹩ (blue triangles), and spatial extent of the filaments (multicolor stars) measured in simulation TI07. Right panel: ﹩\langle {L}_{{\rm{K}}}\rangle ﹩ as a function of filament extent. Colors mark different times in the simulation. The black solid line shows the power-law fit for data points between 2 and 9.5 Gyr, while green lines indicate the 0.1, 0.5, and 0.9 quantiles for additive quantile regression. Red circles mark the observed clusters with extended Hα filaments from McDonald et al. (2010, 2015), with additional X-ray cavity power and associated uncertainties from Rafferty et al. (2006).