Predicted entropy profile for a halo mass of 10¹³ M_⊙ (left panel), 10¹⁴ M_⊙ (central panel), and 10¹⁵ M_⊙ (right panel). The radius has been normalized to the shock (virial) radius. All profiles are normalized at the shock radius. In red we plot a reference powerlaw with slope 1.2, in blue the profile derived from a combination of the functional forms: K(R) = K_v(M_h(R)) and in black the one derived by solving the hydrostatic equilibrium equation.