Abstract
A new method is proposed which enables one to convert the formulas for a uniform multi-component system to those for a non-uniform one. As an application of the method, the expansion formulas of the free energy, potentials of average force and distribution functions for a non-uniform multi-component system are derived in a simple and systematic way. The formulas are obtained both for a continuous and for a lattice system. The formula obtained for the free energy for a continuous system coincides with that given by Arinstein, and the first few terms of the formulas for the free energy and the pair distribution function for a lattice system are identical to those given by Yvon. A procedure to convert the formulas for a continuous system to those for a lattice system and vice versa is given.
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