Rate of core changes as a function of lookback time for three different mass bins according to TNG-Cluster. We define the rate as the number of transformations in a mass and time bin divided by the length of the time interval and number of halos in that bin (details in the text). Orange (blue) lines indicate the rate of changes to higher (lower) core entropy. The bands for each line mark the methodological uncertainty; that is, the variation of the result we obtain when redoing the analysis with a larger and lower threshold of the entropy time derivative. The solid lines show the result for our fiducial choice of threshold. We find no trend with mass and only very weak redshift trends for both type of transformations, but the rate for changes to lower core entropy is overall smaller.