Solution to the Liouville Equation under Equilibrium Conditions

2 Solution to the Liouville Equation under Equilibrium Conditions 

For a system of molecules at equilibrium, the density function is independent of time and the Liouville equation becomes 

we assume a separable solution and that the force is configurational dependent only [F, (r- )]. Thus, we seek a separable, stationary solution to Eq. (4.1) as 

For a system of point particles at equilibrium, the function nn depends only on the separation distances between particles. Functionally, we must have 

In this section, for the sake of simplicity, we will assume that the intermolecular potential function for point particles depends only on the separation distances, i.e.. 

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