Uniformly random sampling of phase space

Consider a model NVT system of particles interacting with the Lennard-Jones potential. We assume that periodic boundary conditions are used and that N is in the order of 10. We also assume that there is an available program subroutine that returns a uniform random number in the interval (0, 1) when called in the main simulation program. 

The steps of an algorithm used to estimate the average excess energy by randomly generating A/triais points in phase space are as follows  

Obtain a point X in configurational phase space by rescaling all C to compute random positions inside the system s volume. 

Specifically, for each particle determine its x position in a cubic simulation box of size L using the following expression  

Drawing 3N different, a random configuration is now generated for all N particles representing a point X in 31V configurational space. 

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