An information-theoretic bound on cosmic coherence in finite-volume simulations

We quantify the physical memory of the cosmic density field using mutual information between $N$-body snapshots at different redshifts, removing a random baseline to isolate gravitational correlations. The shared mutual information rises with scale, peaks near $\simeq L\mathrm{/}8$ (where $L$ is the simulation box size), and declines thereafter. This behaviour is robust to box size and discretization, and identifies the largest coherently retained modes unaffected by missing long-wavelength power, establishing a finite-volume limit on the coherence of cosmic structure with direct implications for homogeneity studies.