For the configurational variables and the thermodynamic observables, the scalings of Eq. 1 only hold exactly in the context of pure-solvent systems with a homogeneous s-value . However, they are still expected to hold approximately for a pure solvent in the AdSoS setup, provided that the s-gradients within the system are sufficiently low. Note, in particular, that the energetic quantities (including the temperature), the relaxation times, and the dielectric permittivity are all invariant upon scaling.