MONTE-CARLO ANNEALING TECHNIQUE FOR THE MINIMIZATION OF THE ONSAGER FREE-ENERGY FUNCTIONAL

A simple Monte Carlo annealing technique is proposed for the minimization of the Onsager Helmholtz free energy functional at the level of the second virial coefficient. Random changes are made to vary a discrete representation of the single particle distribution function f(theta) in order to determine the minimum of the free energy surface. The annealing technique gives results of accuracy comparable with other commonly used minimization methods. The main advantage of the annealing technique is that it is not necessary to assume a particular functional form for f(theta). It is also easy to extend the method to include higher virial coefficients, and to mixtures. We anticipate that this type of technique could be of quite general use for a number of problems involving the minimization of functionals.