Entropy within different radii as a function of the integrated temperature (within R₅₀₀). The entropy is calculated for each halo as the ratio between the mass-weighted temperature and the electron density within that same radius. We calculate the running median for the detected (red), undetected (blue), and full sample (black). We plot the 25^th − 75^th percentiles with the shaded band. The black crosses represent the observational eRASS1 dataset from Bahar et al. (2024). The three images refer to three different radii (i.e. 0.15 R₅₀₀, R₂₅₀₀, R₅₀₀). We ensure halos host at least 80 gas particles within the selected aperture.