Recent physics research published in Nature and further detailed via arXiv examines how Fisher information measures and Shannon entropy track the effective frequency of a single trapped ion confined in a lattice-combined Paul trap. Ground and first excited motional states track the effective frequency $omega_{mathrm{eff}}=omega,sqrt{1-kappa}$, demonstrating how information redistributes between conjugate spaces. Anharmonic Breakdowns: Retaining quartic lattice corrections introduces non-Gaussian wavefunction features, breaking the mutual compensation between Fisher information and Shannon entropy. Ground State (Modified Paul Trap) Fisher Information & Shannon Entropy Tracks effective frequency $omega_{mathrm{eff}}$, driving information redistribution between conjugate spaces. This anharmonic correction breaks the precise mutual compensation between Fisher information and Shannon entropy that normally sustains the complexity invariant.