X-ray observations of groups and clusters reveal an “entropy floor”: the intragroup and intracluster medium show a minimum entropy level, especially in low-mass systems, that is higher than expected from simple gravitational collapse and shock heating in self-similar ΛCDM models (Ponman et al. 1999; Lloyd-Davies et al. 2000). Explaining this excess, quasi-uniform entropy requires additional non-gravitational heating or pre-heating—often attributed to early feedback from supernovae or AGN—but reproducing both the amplitude and radial behavior of the entropy floor across mass and redshift without over-heating dense cores or violating other scaling relations remains challenging for standard ΛCDM-based simulations (Balogh et al. 1999; Valageas et al. 2003).