is clearly reflected in our [[[agn]{}]{}]{} sample, where we also find a good reproduction of the observed $L-T$ slope. This represents a step forward with respect to earlier works. Indeed, previously, two situations emerged: either the self-regulated AGN mechanism preserved the CC structures by largely enhancing the luminosities of clusters colder than 3 keV and, therefore, failing on the $L-T$ relation [@gaspari.etal.2014; @hahn.etal.2015] or, viceversa, the $L-T$ was adequately created at the expenses of a reasonable baryon census in groups and clusters cores [@puchwein.etal.2008; @gaspari.etal.2014].

Evolution of ICM Scaling Relations
==================================

In this Section, we explore the evolution from $z=0$ up to $z=2$ of the six scaling relations: $M-{M_{\rm g}}$, $M-{T_{\rm mw}}$, $M-{T_{\rm sl}}$, $M-{Y_{\rm X}}$, $L-{T_{\rm sl}}$, and $L-M$. All the temperatures are obtained excising the central region ($<0.15$ $R_{500}$) even if excising the core produced a minimal variation. Indeed, the temperature difference is below 1% in our [[[agn]{}]{}]{} sample and below 2% in observational samples [@2012MNRAS.421.1583M] once we compare the temperature measured in the entire sphere within $R_{500}$ or excising the inner core region. Nevertheless, we decide to follow the standard choice, usually made to avoid the influence of the uncertainties related to the status of the core 