In a recent paper (Entropy 2024, 26, 293), Cimmelli makes use of the constitutive equation of Korteweg fluids to justify the introduction of an extended method to the classical Coleman–Noll procedure. He states that this constitutive equation is incompatible with the second law of thermodynamics and that while several different proposals can be found in the literature to circumvent such a problem, all of them modify the energy balance or entropy flux. Here we note that such statements are not completely true.