My best guess would be that the entropy is lowest (zero?) in the case of maximally correlated atoms and would be at maximum if the atoms don't correlate at all.

But the particularities depend on how you describe your system. I mean, the von Neumann entropy is usually defined for density matrices, as far as I know.

von Neumann entropy of a reduced density operator is measure for bi-partite correlations. However, in your case the best measure of particle entanglement between the atoms is the Spin Squeezing.

see,

A. Sørensen, L. M. Duan, J. I. Cirac, and P. Zoller, Na-

ture 409, 63 (2001).

best

ümit.

Thanks Eugene Bagashov. You are right that von Neumann entropy defined for reduced density matrices.

Thanks Ali Hardal. It is a good article refer by you and great suggestion to look after spin squeezing for my case.