Top panel: Cumulative sum of the time difference between each transformation and its closest merger for all TNG-Cluster halos. We separate transformations to higher (orange) and lower (dark blue) core entropy, along with the corresponding random samples (gold and light blue). Bottom panel: Ratio of the true and random samples for each type of transformation from above. Overall, mergers are significantly more likely found within 1 Gyr before a transformation to higher core entropy than in the random sample. In contrast, it is less likely to find a transformation to lower core entropy up to 3.5 Gyr after a merger. This indicates that changes to higher core entropy are strongly correlated with mergers, while changes to lower core entropy may even be anticorrelated. This connection is strongest for the smallest time differences, and much stronger for major mergers (dashed lines) than mini-mergers (dotted lines).