We present first results from high–resolution Tree+SPH simulations of galaxy clusters and groups , aimed at studying the effect of non–gravitational heating on the entropy of the intra–cluster medium ( ICM ) . We simulate three systems , having emission–weighted temperature T _ { ew } \simeq 0.6,1 and 3 keV , with spatial resolution better than 1 % of the virial radius . We consider the effect of different prescriptions for non–gravitational ICM heating , such as supernova ( SN ) energy feedback , as predicted by semi–analytical models of galaxy formation , and two different minimum entropy floors , S _ { fl } = 50 and 100 keV cm ^ { 2 } , imposed at z = 3 . Simulations with only gravitational heating nicely reproduce predictions from self–similar ICM models , while extra heating is shown to break the self–similarity , by a degree which depends on total injected energy and on cluster mass . We use observational results on the excess entropy in central regions of galaxy systems , to constrain the amount of extra–heating required . We find that setting the entropy floor S _ { fl } = 50 keV cm ^ { 2 } , which corresponds to an extra heating energy of about 1 keV per particle , is able to reproduce the observed excess of ICM entropy .