Tuning Pair and Higher-Order Mutual Information Measures in Oscillator Systems with N-Dependent Frequencies

Analytical expressions for pair and higher-order mutual information measures in position and momentum space are examined for many-particle ($N$) coupled oscillator systems in their ground states. These relations reveal that the magnitudes of the statistical correlations monotonically increase with the strength of the particle interaction for all particle numbers ($N$). On the other hand, the magnitudes of the measures monotonically decrease as $N$ increases, when the intensities of the one- and two-body potentials are fixed. However, extremal points appear in the measures as $N$ is varied, when the intensity of the one-body potential is $N$-dependent, and set at $N^{-\alpha }$. Fractional values of $\alpha$ lead to the appearance of extremal points. These results illustrate how the intensity of the one-body potential can be used to tune the behavior of the statistical correlation measures in these systems.