three samples allow us to qualitatively conjecture whether a possible evolution seen on the scaling relations is caused by the environment and the interactions with the large-scale structure distribution, in case of sample-independent results, or by the astrophysical phenomena affecting the ICM, in the other situation of different outcomes depending by the sample.

[$\bullet$  [[[nr]{}]{}]{} (Non-radiative)]{}. These simulations are carried out by the exact code used in [@2015arXiv150207358B]. The main variations with respect to the standard GADGET code include: the choice of a higher-order Wendland $C^4$ kernel function; a time-dependent artificial viscosity scheme; a thermal diffusion term (or artificial conduction) that improves the treatment of contact discontinuities and promotes fluid mixing. The performance of this code with respect to other particle- or grid-based codes is described in [@sembolini.etal.2016b] and [@sembolini.etal.2016a]. These works show how the cluster simulated with the improved GADGET version (G3-XArt) performs in a similar way to grid codes, AREPO, and the most modern SPH schemes.

[$\bullet$  [[[csf]{}]{}]{} (Cooling, Star formation and stellar Feedback)]{}. The radiative runs consider metal-dependent radiative cooling rates accordingly to [@2009MNRAS.399..574W] where 15 different elements (H, He, C, Ca, O, N, Ne, Mg, S, Si, Fe, Na, Al, Ar, Ni) are followed; the effect 