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It is shown that the Shan-Chen (SC) model for non-ideal lattice fluids can bemade compliant with a pseudo free-energy principle by simple addition of agradient force, whose expression is uniquely specified in terms of the fluiddensity. This additional term is numerically shown to provide fairly negligibleeffects on the system evolution during phase-separation. To the best of ourknowledge, these important properties of the SC model were not noted before.The approach developed in the present work is based on a continuum analysis:further extensions, more in line with a discrete lattice theory (X. Shan, {\itPhys Rev E}, {\bf 77} 066702 (2008)) can be envisaged for the future.

Continuum Free-Energy formulation for a class of Lattice Boltzmann multiphase models