Predicted entropy profiles for a halo mass of 10¹³ M_⊙ (blue), 10¹⁴ M_⊙ (red), and 10¹⁵ M_⊙ (black). Dashed lines show entropy from gravitational processes only, solid lines include the effects of pre-heating. The mean entropy profile and intrinsic scatter from the REXCESS sample of galaxy clusters, (Pratt et al. 2010), which features a median mass of M₅₀₀ ∼ 2.5 × 10¹⁴ M_⊙, is reported as an orange shaded region. The region between the 10¹⁴ M_⊙ and 10¹⁵ M_⊙ profiles is shown as a gray shaded region.