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tokens: and the profiles of total velocity dispersion, we finally derive the reconstructed profiles of pseudo-entropy to be compared with the true profiles. Furthermore, in order to verify the accuracy of this procedure based on the Jeans equation to recover pseudo-entropy profiles as a function of the dynamical state of a cluster, we divided our set of simulated haloes into relaxed and disturbed. To carry out this classification, we followed the prescription in Biffi et al. ( 2016 ) and described here in Section 2 . In Fig. B1 , we compare pseudo-entropy profiles recovered from the Jeans equation procedure with the true intrinsic profiles for both relaxed and disturbed systems from the Hydro-1x simulation. In the right-hand panels, we show their density maps in logarithmic scale traced by the DM particles in two clusters within the 0.5 r vir spheres (in white). In each of the two panels on the left, we compare recovered and intrinsic profiles of S ( r ) for both the selected cluster (solid lines), whose density map is reported on the right, and the entire cluster sample (dashed lines). Upper panels display the profiles for relaxed clusters, while lower panels are for disturbed systems. The solid lines are specific to the single cluster, being in cyan the true profile and in orange the one produced by the Jeans equation procedure while the dotted lines refer to the median values of all 29 clusters in the simulation set. In the upper panel, we see that true and Jeans equation profiles overlap at almost all radii, showing that the Jeans equation procedure has correctly reproduced the true profile, which is also in line with the median result. In the lower panel, we show the same profiles but when obtained for a cluster labelled as ‘disturbed’, since a major merger is occurring as shown by its density map. In this cluster, the true profile consistently deviates from the median and the Jeans equation profiles. The latter, in turn, suffers a shift in normalization but not in the slope with respect to the median profiles. Figure B1. On the left: pseudo-entropy profiles (DM particles) for a relaxed and a disturbed cluster in the Hydro-1x simulation at z = 0. The dashed lines are obtained by stacking the true profiles (in cyan) or those obtained by the Jeans equation procedure (in orange), while the solid lines are for the profiles of the specific cluster. On the right: density maps in logarithmic scale traced by the DM particles in the same objects. The brightest colours indicate the areas at higher density. The white circles identify the 0.5 r vir spherical region centred on the cluster centre as computed by SubFind. To quantitatively describe the differences between recovered and true pseudo-entropy profiles, we follow the same procedure described in Section 3 to fit a power-law profile, which depends on two parameters, and concentrate our interest on the accuracy in recovering the slope α. In the first two lines of Table B1 , we report the true and the