Figure 6.

Block density analysis of a Lennard-Jones fluid. (A) Image of the local densities of a projected Lennard-Jones fluid with a block size b = σ. Each projected molecule is indicated by a point. Although σ is the hard-sphere radius of the particles, more than one particle can be found per block as we deal with projections. (B) The reduced fourth-order cumulant, U_b (Eq. 3), approaches the value zero for large b, indicating a Gaussian density distribution above the typical interaction length scale, ξ = σ, of the system. (C) The compressibility of the system. The inset shows that for length scales larger than σ, the block-size-dependent compressibility, κ_b, can be extrapolated to the limit $b\to \infty$, yielding the isothermal compressibility, κ_T/κ₀ = 0.45, of the system. Compressibilities are scaled with the isothermal compressibility of an ideal gas, κ₀, to obtain independence of the system average density.